
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 \( \triangle ABC \), the lengths of the three sides are \( a, b, \) and \( c \). If \( \angle A = 60^\circ \), then
$$
S_{\triangle ABC} = \frac{\sqrt{3}}{4} \left[a^2 - (b-c)^2 \right]
$$

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