Synonyms for Assess:

n.

add up, charge, exact, impose, project, prove. contemplate, levy, obligation, over, ponder, put, think out, think over, willing, take a long hard look at someone/something, take something into consideration. assay, size up. assess (noun)
appraise, evaluate, measure, tax, valuate, value.

v.

assign fee, (verb)
evaluate, exact, impose, levy, tax.
calculate (verb)
account, add, appraise, approximate, calculate, compute, conclude, consider, count, deduce, determine, divide, enumerate, estimate, evaluate, figure, gauge, guess, infer, judge, measure, multiply, plan, plot, presume, program, quantify, quantize, rank, rate, rationalize, reckon, schedule, scheme, score, study, sum, suppose, surmise, systematize, tally, think, total, triangulate, value, weigh.
evaluate, determine (verb)
appraise, assay, compute, determine, estimate, figure, gauge, guess, judge, rate, reckon, size up, valuate, value, weigh.
judge (verb)
adjudicate, arbitrate, decide, find, mediate, pronounce, referee, resolve, rule, sentence.

Other synonyms:

add up, ponder, project, size up, think out, think over. contemplate, impose, levy. put. analyze
assay.
gauge
gauge.
judge
referee.
measure
quantify.
valuate
valuate.
Other relevant words:
add up, assay, charge, contemplate, exact, impose, levy, obligation, over, ponder, project, prove, put, size up, tax, valuate, willing.