
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 a triangular prism (not necessarily right) with triangular bases, the sum of the areas of two bases and one lateral face is 36. Assume the prism's base triangle sides are $a$ and $b$ with included angle $\theta$ (which is not a right angle), and that the prism has altitude $h$. Find the maximum volume of the prism.

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