
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
Consider a regular octagon in which a square is inscribed. The square and the octagon share one common side. What is the degree measure of $\angle ABC$? Diagram is not required, but for clarity: 
- Let $A$, $B$ be two consecutive vertices of the octagon on one side of the shared side.
- Let $C$ be the adjacent vertex of the square to $B$ along the shared side.

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