
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
A square and a regular octagon are coplanar and share a common side $\overline{AD}$, as indicated. Determine the degree measure of the exterior angle $BAC$. Assume the diagram and labeling analogous to the given heptagon problem, where $A$ and $D$ are vertices on the common side of the square and octagon, and $B$ is a vertex of the octagon touching side $AB$.

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