
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
Find the ratio of the volume of a regular hexagonal pyramid to the volume of a regular triangular pyramid, given that the sides of their bases are equal and their slant heights are twice the length of the sides of the base.

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