#1 assess v. [measure, evaluate, valuate, appraise, value] evaluate or estimate the nature, quality, ability, extent, or significance of; "I will have the family jewels appraised by a professional"; "access all the factors when taking a risk". wn
#2 assess v. charge (a person or a property) with a payment, such as a tax or a fine. wn
#3 assess v. [tax] set or determine the amount of (a payment such as a fine). wn
#4 assess v. estimate the value of (property) for taxation; "Our house hasn't been assessed in years". wn
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