
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 \(BCFG,\) as shown. Determine the number of degrees in \( \angle FAG \) (not pictured). Assume the square and triangle are in the same plane and \( \angle BCF \) is a right angle.
[asy]
pair pA, pB, pC, pF, pG;
pA = (0, 0);
pB = pA + dir(300);
pC = pA + dir(240);
pF = pC + dir(270);
pG = pB + dir(270);
draw(pA--pB--pC--pA);
draw(pB--pC--pF--pG--pB);
label("$A$", pA, N);
label("$B$", pB, E);
label("$C$", pC, W);
label("$F$", pF, SW);
label("$G$", pG, SE);
[/asy]

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