
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 parabola $y^2 = 4x$, let line $l$ with a slope of $1$ intersect the parabola at points A and B, and intersect the x-axis at point M. The midpoint of chord AB is P.
(1) If M(2, 0), find the equation of the circle with diameter AB.
(2) Let M(m, 0). If the point P satisfies $\frac {1}{|AM|}+ \frac {1}{|BM|}= \frac {1}{|PM|}$, find the value of $m$.

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