
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
The base of a triangular prism \(S-ABC\) is an equilateral triangle. The lateral edge \(SA = 1\), and the projection of \(A\) onto the lateral face \(SBC\) is the orthocenter \(H\) of \(\triangle ABC\). Determine the maximum value of \(V_{S-ABC}\).

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