
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 square \( PQRS \) with a side length greater than \( 20 \text{ cm} \), there is a largest possible circle \( O \) inscribed within the square. If a point \( T \) on the circumference of circle \( O \) is \( 8 \text{ cm} \) away from side \( PS \) and \( 9 \text{ cm} \) away from side \( PQ \), what is the radius of circle \( O \) in cm?

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