
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
Consider a shaded region made of 13 unit squares, resting along the $x$-axis and the $y$-axis. This region forms a shape that consists of a vertical strip of 7 unit squares from the origin upwards and a horizontal strip of 6 unit squares from the origin to the right. The shaded region is rotated about the $x$-axis to form a solid. Calculate the volume of the solid formed, and express your answer in terms of $\pi$.

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