Some adjectives have a strong, formal adverb partner meaning totally or completely: utterly convinced, fully aware, entirely different. Learn these as whole units, because they are what formal writing reaches for. A generic very or really is not wrong: very aware and completely convinced are ordinary English. It is just weaker, so it flattens a sentence that wanted force.
Adverbs that mean "completely"
utterly convinced /ˈʌtərli kənˈvɪnst/ — After reading the report, I'm utterly convinced that we chose the right supplier.
fully aware /ˈfʊli əˈwɛr/ — The committee was fully aware of the risks before they voted.
entirely different /ɪnˈtaɪərli ˈdɪfrənt/ — The second draft took an entirely different approach to the problem.
Not ""I am very convinced that this is the right decision." (grammatical, but not the natural pairing)" — say ""I am utterly convinced that this is the right decision."". With convinced, the idiomatic partner is utterly, not 'very'. These adverbs are fixed to their adjective.
Try it: Which phrase sounds most natural in formal English: "She was ___ of the deadline and planned accordingly."? (fully aware / broadly aware / strongly aware) Answer: fully aware — 'Fully aware' means completely aware, which is what planning ahead for the deadline shows. 'Broadly aware' would mean she knew roughly about it, which is weaker than her planning suggests, and 'strongly aware' isn't a natural pairing, 'strongly' doesn't go with 'aware'.
Adverbs for deep and extreme intensity
Other adjectives call for an adverb that signals depth or an extreme degree. Habits and beliefs are deeply rooted; a problem can be extremely difficult; something unusual is exceedingly rare. A plain very is not an error here. It is simply weaker, so formal writing usually reaches past it for one of these.
deeply rooted /ˈdipli ˈrutɪd/ — These attitudes are deeply rooted in the region's history.
extremely difficult /ɪkˈstrimli ˈdɪfɪkəlt/ — Balancing the budget without cuts proved extremely difficult.
exceedingly rare /ɪkˈsidɪŋli ˈrɛr/ — A find of this quality is exceedingly rare in the field.
Not ""The problem is strongly rooted in our culture." (understood, but not the standard pairing)" — say ""The problem is deeply rooted in our culture."". Rooted partners with deeply, not 'strongly'. Depth adverbs go with things that are established over time.
Try it: Which option is the most idiomatic, formal way to describe something very unusual? (exceedingly rare / widely rare / deeply rare) Answer: exceedingly rare — 'Exceedingly rare' is the formal pairing for something extremely uncommon. 'Widely rare' contradicts itself, since 'widely' means across many places, and 'deeply rare' misapplies a depth adverb, 'deeply' pairs with things like 'rooted' or 'affected', not 'rare'.
Try it: Complete the sentence naturally: "Persuading everyone to agree turned out to be ___." (extremely difficult / strongly difficult / deeply difficult) Answer: extremely difficult — 'Extremely difficult' is the standard extreme-intensity pairing for 'difficult'. 'Strongly difficult' isn't an English collocation. 'Deeply difficult' is possible, but it means difficult at a fundamental level rather than very difficult, so it doesn't answer what the sentence is asking.
Adverbs that push the degree high
Two adverbs place an adjective high on a scale, and each one is fixed to its partner. Highly puts something far up that scale, so a subject people argue about is highly contentious. Overwhelmingly goes further: it means so far up the scale that the other side barely registers, so results that almost everyone welcomes are overwhelmingly positive. Both belong to formal writing, and a generic very in their place drains the force out.
highly contentious /ˈhaɪli kənˈtɛnʃəs/ — Building over part of Senville Park became a highly contentious issue at the council meeting.
overwhelmingly positive /ˌoʊvərˈwɛlmɪŋli ˈpɑzətɪv/ — Feedback on the redesigned Magaff Library was overwhelmingly positive.
Not ""The proposal was very contentious and the response was very positive." (grammatical, but flat, and it loses the difference between the two degrees)" — say ""The proposal was highly contentious and the response was overwhelmingly positive."". Highly marks a high degree; overwhelmingly marks a degree so high that nothing counters it. A single very cannot carry that difference.
Try it: Ninety-eight percent of readers rated the new service well. Which phrase reports that figure most precisely? (overwhelmingly positive / highly positive / utterly positive) Answer: overwhelmingly positive — 'Overwhelmingly' is the partner that says the favorable side is so large the rest barely counts, which is what ninety-eight percent means. 'Highly positive' marks a high degree but not a one-sided one, so it understates the figure. 'Utterly' prefers negative or all-or-nothing adjectives (utterly useless, utterly convinced), so it sits oddly on a scale word like 'positive'.
How many people, or how little effort
These two adverbs look similar in a dictionary but answer different questions, so keep them apart. Widely answers how many people or places, so a fact most specialists accept is widely acknowledged. Readily answers how little effort it takes, so information you can find in one click is readily available. Swapping them breaks the sense: readily acknowledged by experts changes the claim from how many agree to how willingly they admitted it.
widely acknowledged /ˈwaɪdli əkˈnɑlɪdʒd/ — It is widely acknowledged that the early results were misread.
readily available /ˈrɛdəli əˈveɪləbəl/ — Train timetables are readily available at every station in Haffenville.
Not ""The findings are readily acknowledged across the field." (says the field admitted them willingly, not that most of it agrees)" — say ""The findings are widely acknowledged across the field."". Widely counts people; readily measures effort. Choose by which question the sentence is answering.
Try it: The forms can be downloaded in seconds from the Haffenville council website. Which phrase describes them? (readily available / widely available / fully available) Answer: readily available — 'Readily' is the fixed partner here because the sentence is about how little effort the forms take to get. 'Widely available' is a real phrase, but it would claim the forms can be found in many places, which is a different point from downloading them in seconds. 'Fully available' exists, but it means available in full rather than easy to get, so it answers a different question again.