
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 the circular sector \( OAB \), the central angle of which is \( 45^{\circ} \), a rectangle \( KMRT \) is inscribed. Side \( KM \) of the rectangle lies along the radius \( OA \), vertex \( P \) is on the arc \( AB \), and vertex \( T \) is on the radius \( OB \). The side \( KT \) is 3 units longer than the side \( KM \). The area of the rectangle \( KMRT \) is 18. Find the radius of the circle.

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