
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
Given an equilateral triangle $ABC$ and a square $BCFG$ such that they share a common side $BC$, find the measure of $\angle FAG$ where point $F$ is on the extension of side $AB$ and point $G$ is on the extension of side $AC$. Assume $F$ and $G$ are such that $BF = AB$ and $CG = AC$.

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