
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 ellipse $\frac{{x}^{2}}{8}+\frac{{y}^{2}}{4}=1$, point $M(2,1)$ is the midpoint of the chord $AB$ of the ellipse.<br/>$(1)$ Find the equation of the line $AB$;<br/>$(2)$ Find the length of the chord $AB$.

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