
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 consisting of 13 unit squares. This region is located in the first quadrant, beginning along the y-axis and stretching rightwards with the following dimensions: 1 unit wide and 5 units high from the origin and an attached section 3 units wide and 2 units high. This shape is rotated about the x-axis. Calculate the volume of the solid formed.

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