
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 that $\angle A=30^\circ$ and $\angle BAC = \angle BCA$, in triangle ABC, determine how many degrees $\angle E + \angle G$ is. Assume triangle EFG is located inside triangle ABC such that $\angle EFG = \angle EGF$. Assume further $\angle EFA = \angle E$ and $\angle GFB = \angle G$. [asy]
/* Modified problem */
pair A=(0,0), B=(1,0), C=(0.5,0.8);
draw(A--B--C--cycle);
label("$A$", A, SW);
label("$B$", B, SE);
label("$C$", C, N);
label("$E$", (0.2, 0.2));
label("$F$", (0.5, 0.4));
label("$G$", (0.8, 0.2));
[/asy]

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