
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
Sector $PQR$ is a quarter of a circle with a radius of 5 cm. An inscribed circle is tangent to the two sides and the arc of this sector. Determine the radius of this inscribed circle. Express your answer in simplest radical form.

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