
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
What is the maximum volume of pyramid \( S A B C \), where \( A B = 5 \), \( A C = 8 \), and \(\sin \angle B A C = \frac{3}{5} \), if all lateral edges \( S A, S B, S C \) form equal angles with the base plane, not exceeding \(60^{\circ}\)?

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