
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
Isosceles triangle $ABC$ (where $AB=AC$ and $BC$ forms the base) and square $BCFG$ are coplanar, with $B$ and $C$ shared by both shapes. Base angles of the triangle, $\angle ABC$ and $\angle ACB$, are $70^\circ$ each. Determine the measure of $\angle FAG$.

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