
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
The shaded region shown consists of a configuration of 18 unit squares, arranged such that there are two separate groups. One group, 10 squares in a straight line along the $y$-axis, and the other group, 8 squares resting along the $x$-axis from (1,2) to (9,2). The shaded region is rotated about the $x$-axis to form a solid. What is the volume of the resulting solid in cubic units? Express your answer in terms of $\pi$.

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