
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 $LOQ$ when polygon $\allowbreak LMNOPQRS$ is a regular octagon? [asy]
draw((-2,0)--(-1,1.73205081)--(1,1.73205081)--(3,1.73205081)--(4,0)--(3,-1.73205081)--(1,-1.73205081)--(-1,-1.73205081)--cycle);
draw((-1,-1.73205081)--(3,1.73205081)--(1,-1.73205081)--cycle);
label("L",(-1,-1.73205081),SW);
label("M",(-2,0),W);
label("N",(-1,1.73205081),NW);
label("O",(1,1.73205081),N);
label("P",(3,1.73205081),N);
label("Q",(4,0),E);
label("R",(3,-1.73205081),S);
label("S",(1,-1.73205081),S);
[/asy]

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