
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 right-angle coordinate system, the points

$$
A(0,9), \quad B(6,3), \quad C\left(-\frac{1}{3},-1\right) \quad \text { and } D\left(3,-\frac{7}{2}\right)
$$

are given. Determine the point $P$ such that $P A = P B$ and $P C : P D = 2 : 3$.

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