
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
In $\triangle ABC$, $\angle C = 90^{\circ}$, $AC = 10$, and $BC=24$. Squares $ACDE$ and $BCFG$ are constructed outside of the triangle on sides AC and BC, respectively. The points $D, E, F, G$ lie on a circle. What is the perimeter of $\triangle ABC$?
A) 52
B) 58
C) 60
D) 64

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