
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 equation of circle $O$ is $x^2 + y^2 = 2$, and the equation of circle $M$ is $(x - 1)^2 + (y - 3)^2 = 1$. A tangent line $PA$ is drawn from any point $P$ on circle $M$ to circle $O$. If the other intersection point of line $PA$ with circle $M$ is $Q$, then when the length of chord $PQ$ is maximized, the slope of line $PA$ is ______.

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