
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 sphere of radius 3 is encased within a square pyramid such that it is tangent to all four triangular faces of the pyramid and just contacts the base of the pyramid. The height of the pyramid is 9. Determine the edge-length of the base of the pyramid.
- **A)** 3
- **B)** 4.5
- **C)** 6
- **D)** 7.5

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