
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 region consisting of 15 unit squares arranged along the $x$-axis and the $y$-axis as shown. The region is rotated about the $y$-axis to form a solid. Calculate the volume of the resulting solid. The region is described as follows: a vertical strip of 7 unit squares high and 1 unit wide along the y-axis, and a horizontal strip of 3 unit squares wide and 2 units high along the x-axis, starting from the top of the vertical strip.

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