
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 quadrilateral pyramid is a rectangle with one side equal to \(a\), and the lateral edges of the pyramid are equal to \(b\). Find the maximum volume of such pyramids.

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