
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 that the right focus of the ellipse $E: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ is $F$, the length of the minor axis is $2$, and $M$ is a moving point on the ellipse $E$ with the maximum value of $|MF|$ being $\sqrt{2}+1$.

1. Find the equation of the ellipse $E$.
2. Let the coordinates of the point $M$ (not on the coordinate axes) be $(x_{0},y_{0})$, and let $A$ and $B$ be two distinct points on the ellipse $E$ different from $M$ such that the line $x=x_{0}$ bisects $\angle AMB$. Express the slope of the line $AB$ in terms of $x_{0}$ and $y_{0}$.

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