
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
An equilateral triangle $ABC$ shares a common side $BC$ with a square $BCDE$. A semicircle with diameter $BC$ is placed such that it extends outward from the square, and point $F$ is the midpoint of arc $BC$. Find the number of degrees in $\angle FAE$.

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