
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 a circle M with center M(-1, 2), the chord intercepted by the line $y = x + 4$ on circle M has a length of $\sqrt{2}$. Point P is on the line $l: y = x - 1$.
(1) Find the standard equation of circle M;
(2) Suppose point Q is on circle M, and it satisfies $\overrightarrow{MP} = 4\overrightarrow{QM}$, find the coordinates of point P.

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