
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 is formed by 16 unit squares and rests along the $x$-axis and the $y$-axis. The shaded region is rotated about the $x$-axis to form a solid. The region consists of a 6-unit high and 1-unit wide column along the y-axis, and a 3-unit high and 3-unit wide column along the x-axis starting from the top of the first column. In cubic units, what is the volume of the resulting solid? Express your answer in terms of $\pi$.

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