
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 points $A(4,-3)$ and $B(2,-1)$, and line $l$: $4x+3y-2=0$, there exists a point $P$ in the coordinate plane such that $|PA|=|PB|$, and the distance from point $P$ to line $l$ is $2$. Determine the coordinates of point $P$.

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