
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 $l: 4x + 3y - 2 = 0$.

(1) Find the equation of the locus of point $P$ such that $|PA| = |PB|$ in the Cartesian plane.

(2) Find the coordinates of point $P$ such that $|PA| = |PB|$ and the distance from point $P$ to line $l$ is $2$ in the Cartesian plane.

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