Synonyms for Assess:

n.

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

v.

assign fee, (verb)
exact, impose, tax, evaluate, levy.
evaluate, determine (verb)
figure, value, weigh, estimate, size up, judge, valuate, guess, compute, determine, gauge, reckon, rate, appraise, assay.
judge (verb)
find, sentence, decide, rule, resolve, adjudicate, arbitrate, mediate, referee, pronounce.

Other synonyms:

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