
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 is inscribed in a hemisphere so that one base of the cylinder is coplanar with the hemisphere's base. The radius of the hemisphere is increased to 7, while the radius of the cylinder remains 2. Calculate the height of the cylinder if the top base of the cylinder coincides with the top of the hemisphere.

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