
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 the line l: y = 2x + 1, and two points A(-2, 3), B(1, 6), point P is on line l.
(1) If the distance from point P to points A and B is equal, find the coordinates of point P.
(2) Find the minimum value of |PA| + |PB|.

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