
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 parabola $C: y^2 = 2px$ ($p>0$), with the focus $F$ and directrix $l$, if point $A$ on the parabola $C$ has an x-coordinate of $3$ and the distance from point $A$ to the directrix $l$ is $5$:
1. Find the equation of parabola $C$.
2. Find the equation of the line that contains the chord whose midpoint is $M(3, 2)$.

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