
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 regular pentagon $ABCDF$ shares a common side $BC$ with a square $BCGH$, as pictured. Find the number of degrees in $\angle GAF$. [asy]
pair pA, pB, pC, pG, pH, pD, pF;
pA = (0, 0);
pB = pA + dir(288);
pC = pA + dir(216);
pG = pC + dir(270);
pH = pB + dir(270);
pD = pA + dir(144);
pF = pA + dir(72);
draw(pA--pB--pC--pD--pF--pA);
draw(pB--pC--pG--pH--pB);
label("$A$", pA, N);
label("$B$", pB, E);
label("$C$", pC, W);
label("$G$", pG, SW);
label("$H$", pH, SE);
label("$D$", pD, NE);
label("$F$", pF, NW);
[/asy]

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