
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 $\dfrac {x^{2}}{16}+ \dfrac {y^{2}}{4}=1$, a point $M(2,1)$ inside the ellipse, and a line passing through $M$ intersecting the ellipse at points $A$ and $B$. If $M$ is the midpoint of chord $AB$, does such a line exist? If it does, find its equation; if not, explain why.

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