
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 hemisphere with a radius of 3 rests on the base of a triangular pyramid of height 9, and the hemisphere is tangent to all three faces of the pyramid. Calculate the length of each side of the base of the equilateral triangle.

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