
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 circular iron sheet with a radius of $3\sqrt{3}$ is cut into a sector with a central angle of α. The remaining sector is used to form a conical container with height $h$ and volume $V$.

1. Find the function $V(h)$ that describes the volume in terms of the height.
2. Determine the central angle α that maximizes the container's volume $V$.

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