
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 consists of rectangles organized as follows and rests along the $x$-axis and the $y$-axis. The region is bounded by $y=4$ from $x=0$ to $x=1$, and by $y=3$ from $x=1$ to $x=5$. This region is rotated about the $x$-axis to create a solid. Calculate the volume of the solid formed in cubic units. Express your answer in terms of $\pi$.

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