
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 shaded region in the coordinate plane consists of 12 unit squares. This region is situated such that it touches both the $x$-axis and the $y$-axis. The configuration is as follows: there are 6 unit squares stacked vertically starting at the origin, and to the right of the topmost square, there are 6 unit squares arranged in a 2x3 rectangle. This region is rotated about the $x$-axis. Calculate the volume of the resulting solid in cubic units in terms of $\pi$.

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