Death Blow and Advanced

[Marcelo Batista]

If the character Corvus Glaive makes a Death Blow attack and decides to use Advanced, can he use the movement tool S to climb the nearby size 4 building, or will he not be able to climb because the specific text of the card Advanced in this case would be a Climb action?

[Thoras]

If a special rule provides you a specific type of movement, you must follow the rules for that specific type of movement.

This means that no, he will not be able to perform a Climb when granted an Advance (unless some other special rule allowed him to do so).