
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 conical flask has a base radius of $15$ cm and a height of $30$ cm. The flask is filled with a liquid to a height of $10$ cm from the base, and a sphere is inscribed such that it just touches the liquid surface. What is the radius of the sphere? Express your answer in cm.

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