
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 point $P(2,-1)$ is the midpoint of the chord intercepted by the ellipse $\frac{{x}^{2}}{8}+\frac{{{y}^{2}}}{4}=1$, determine the equation of the line on which the chord lies.

A) $x=2$
B) $y=x-3$
C) $y=-x+1$
D) $y=-x-3$

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