
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
Given a parallelogram $ABCD$ with two vertices $A(0,0)$ and $B(4,-3)$, point $P$ divides diagonal $AC$ internally in the ratio $2:1$. If point $D$ moves on the circumference of a circle centered at $A$ with radius 3, determine the locus of point $P$.

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