
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 18 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 first part of the shaded region extends from $y=0$ to $y=6$ along the $y$-axis and from $x=0$ to $x=1$ along the $x$-axis. The second part extends from $y=0$ to $y=3$ along the $y$-axis and from $x=1$ to $x=5$ along the $x$-axis. In cubic units, what is the volume of the resulting solid? Express your answer in simplest form in terms of $\pi$.

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