
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. The base angle of the isosceles triangle in this vertical cross section is 45 degrees. Find the height of the cone.

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