
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 circle $O$: $x^{2}+y^{2}=1$ and point $A(-2,0)$, if point $B(b,0)$ ($b \neq -2$) and constant $\lambda$ satisfy: for any point $M$ on circle $O$, $|MB|=\lambda|MA|$, then:
(I) $b=$ \_\_\_\_\_\_;
(II) $\lambda=$ \_\_\_\_\_\_.

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