
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 $\triangle PQR$, $\angle Q = 90^\circ$, $PQ = 9$, and $QR = 12$. Squares $PQAB$ and $QRCD$ are constructed outside of the triangle. If points $A$, $B$, $C$, and $D$ all lie on a circle, determine the radius of this circle.
A) $6$
B) $6\sqrt{2}$
C) $12$
D) $9$
E) $9\sqrt{2}$

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