
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 $O: x^2 + y^2 = 1$ and a point $A(-2, 0)$, if there exists a fixed point $B(b, 0)$ ($b \neq -2$) and a constant $\lambda$ such that for any point $M$ on the circle $O$, it holds that $|MB| = \lambda|MA|$. The maximum distance from point $P(b, \lambda)$ to the line $(m+n)x + ny - 2n - m = 0$ is ______.

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