
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 $C: (x+1)^2 + (y-2)^2 = 2$, a point $P(x_1, y_1)$ outside the circle is connected to the circle by a tangent line at point $M$. $O$ is the origin of the coordinates, and $|PM| = |PO|$. Find the coordinates of point $P$ when $|PM|$ reaches its minimum value.

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