
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 right circular cylinder with an unknown radius is inscribed in a hemisphere with diameter 10 so that its bases are parallel to the base of the hemisphere. Find the height of the cylinder if the radius of its base is 3.

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