
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
Given a triangle  $OAB$  with the vetices  $O(0,\ 0,\ 0),\ A(1,\ 0,\ 0),\ B(1,\ 1,\ 0)$  in the  $xyz$  space.
Let  $V$  be the cone obtained by rotating the triangle around the  $x$ -axis.
Find the volume of the solid obtained by rotating the cone  $V$  around the  $y$ -axis.

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