
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
What is the degree measure of angle $PTV$ when polygon $PQRSTUVW$ is a regular octagon? 

[asy]
draw((1,0)--(0.7071,0.7071)--(0,1)--(-0.7071,0.7071)--(-1,0)--(-0.7071,-0.7071)--(0,-1)--(0.7071,-0.7071)--cycle);
draw((0,-1)--(0.7071,0.7071)--(-0.7071,-0.7071)--cycle);
label("P",(0.7071,-0.7071),SE);
label("Q",(1,0),E);
label("R",(0.7071,0.7071),NE);
label("S",(0,1),N);
label("T",(-0.7071,0.7071),NW);
label("U",(-1,0),W);
label("V",(-0.7071,-0.7071),SW);
label("W",(0,-1),S);
[/asy]

Present the answer in LaTex format: \boxed{Your answer}
user