
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 point \( A \) has coordinates \( (0,3) \), and points \( B \) and \( C \) are on the circle \( O: x^{2}+y^{2}=25 \), satisfying \(\angle B A C=90^{\circ}\). Find the maximum area of \(\triangle A B C\).

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