
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
Triangle $PQR$ has $P=(0,0)$, $R=(6,0)$, and $Q$ in the first quadrant. Additionally, $\angle QRP=90^\circ$ and $\angle QPR=45^\circ$. Suppose that $PQ$ is rotated $60^\circ$ counterclockwise about $P$. What are the coordinates of the image of $Q$?
A) $( -3\sqrt{3},9)$
B) $(3 - 3\sqrt{3}, 3 + 3\sqrt{3})$
C) $( -3,9\sqrt{3})$
D) $(6,12)$

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