
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 $\Gamma: \frac{x^{2}}{4}+ \frac{y^{2}}{3}=1$, a line $l$ passes through the point $P(1,1)$ and intersects the ellipse $\Gamma$ at points $A$ and $B$. If the chord $AB$ has point $P$ as its midpoint, find the equation of line $l$ (write in general form).

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