
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 two vertices $A(0,0)$ and $B(4,-3)$ of a parallelogram, and a point $P$ which divides the diagonal $AC$ in the ratio $2:1$, when point $D$ moves on the circumference of a circle centered at $A$ with radius 3, find the trajectory of point $P$.

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