
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 and a right circular cone are inscribed in a hemisphere of radius 7 such that the bases of both the cylinder and cone are parallel to the base of the hemisphere. The radius of the cylinder is 3. If the top circle of the cylinder is the base of the cone and both shapes touch the hemisphere's inside surface, what is the height of the cylinder?

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