
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
A rectangle with sides $a$ and $b$ rotates around an axis passing through its vertex, parallel to the diagonal that does not pass through this vertex. Find the volume of the resulting solid of revolution. Given: $ABCD$ is a rectangle, $|AB|=a$, $|AD|=b$, $l$ is the axis of rotation, $A \in l$, $l \parallel [BD]$. Find: $V_{ABCD}$, the volume of the solid of revolution.

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