
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
There is a shaded region consisting of a composite of squares and rectangles how positioned over the $x$-axis and the $y$-axis. The region is composed of a square of side 4 units and a rectangle of 3 units by 5 units. It is rotated about the $y$-axis to form a solid. Calculate the volume of the resulting solid.

![Diagram of Regions](https://via.placeholder.com/150x100.png) [Imagine this as an updated region diagram fitting the new problem's description.]

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