Real Dictionary

assess
verb: When you assess a person, thing, or situation, you consider them in order to make a judgment about them.
verb: When you assess the amount of money that something is worth or should be paid, you calculate or estimate it.

assess in American English
to set an estimated value on (property, etc.) for taxation
transitive verb: to estimate officially the value of (property, income, etc.) as a basis for taxation

assess in British English
to judge the worth, importance, etc, of; evaluate