
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
An opaque hemisphere of radius 3 cm rests on a square pyramid of height 9 cm. The hemisphere is tangent to each of the four lateral faces of the pyramid. What is the edge-length of the base of the pyramid?
A) $4.5$ cm
B) $5.5$ cm
C) $6.5$ cm
D) $7.5$ cm

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