
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 cone has a volume of $16384\pi$ cubic inches and the vertex angle of the vertical cross section is 90 degrees. What is the height of the cone? Express your answer in simplified radical form if necessary.

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