
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 an oblique prism is an equilateral triangle with side length \(a\). One of the lateral faces of the prism is perpendicular to the base plane and is a rhombus with a diagonal of length \(b\). Find the volume of the prism.

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