
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
In a semicircle with a radius of 18 cm, a semicircle with a radius of 9 cm is constructed on one half of the diameter. A circle is inscribed such that it touches the larger semicircle internally, the smaller semicircle externally, and the other half of the diameter. Find the radius of this inscribed circle.

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