
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 $F$ is the focus of the parabola $y^{2}=2px (p > 0)$, and point $M(2,m)$ is on the parabola $E$ with $|MF|=3$.

1. Find the equation of the parabola $E$.
2. Find the equation of the line containing the chord with point $N(1,1)$ as its midpoint.

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