Collins

assess
verb [transitive]
1 to judge the worth, importance, etc., of; evaluate
2 [foll by at] to estimate the value of (income, property, etc.) for taxation purposes
example: the estate was assessed at three thousand pounds
3 to determine the amount of (a fine, tax, damages, etc.)
4 to impose a tax, fine, etc., on (a person or property)
[ETYMOLOGY: 15th Century: from Old French assesser, from Latin assidere to sit beside, from sedere to sit]

evaluate verb [transitive]
1 to ascertain or set the amount or value of
2 to judge or assess the worth of; appraise
3 (Maths) (logic) to determine the unique member of the range of a function corresponding to a given member of its domain
[ETYMOLOGY: 19th Century: back formation from evaluation, from French, from evaluer to evaluate; see value]
e"valu'ation noun
e'valu"ator noun