assess

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"

charge (a person or a property) with a payment, such as a tax or a fine

set or determine the amount of (a payment such as a fine)

estimate the value of (property) for taxation; "Our house hasn't been assessed in years"