
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 triangle \( \triangle ABC \) is inscribed in a circle of radius 4 cm. Suppose that \( \angle A = 60^\circ \), \( AC - AB = 4 \) cm, and the area of \( \triangle ABC \) is \( x \) cm\(^2\). Find the value of \( x^2 \).

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