
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 solid is formed by a cylinder of radius 3 units and unknown height \( L \), capped at one end by a hemisphere of the same radius and at the other end by a cone with a height of \( \frac{L}{2} \). The combined volume of the solid is \( 180 \pi \) cubic units. Determine the height \( L \) of the cylinder.
A) 12
B) 14
C) 15.5
D) 18
E) 20

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