
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 the triangular pyramid $S-A B C$, $S A = 4$, $S B \geq 7$, $S C \geq 9$, $A B = 5$, $B C \leq 6$, and $A C \leq 8$. What is the maximum volume of the triangular pyramid $S-A B C$?

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