
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 first quadrant consists of 11 unit squares along the $x$-axis and $y$-axis. It includes a rectangle of height 4 and width 1, and a rectangle of height 3 and width 3. Additionally, there's a right triangle with base 1 and height 3 attached to the top of the 1x4 rectangle. This entire region is rotated about the $x$-axis to form a solid. Calculate the volume of the resulting solid in cubic units, expressed in terms of $\pi$.

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