
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 lines l₁: 2x - y + 2 = 0 and l₂: x + 2y - 4 = 0, and point P(1, m).
(I) If the distance from point P to lines l₁ and l₂ are equal, find the value of the real number m.
(II) When m = 1, it is known that line l passes through point P and intersects lines l₁ and l₂ at points A and B, respectively. If P bisects the line segment AB, find the coordinates of points A and B, and the equation of line l.

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