You should count on the purchase price being equal to the addressed value because that’s what the county will base your assessment off of. And if they go higher, you can always point to the purchase price in your defense of what was the FMV.
Then you use that in the “proper” calculation which depends on your state process to determine the assessed value from the FMV. Typically there is a local value (FMV) and an adjustment factor or equalization factor based on how the county relates to the state as a whole.
Then the equalized value is assessed at the local millage rate.
What the previous owner paid is irrelevant but a copy of their tax statements will give you the formulas.
Typically these are public records and available online.