
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 $y^2=2px$ ($p>0$) passes through the point $(4, -4)$.
1. Find the value of $p$;
2. If a line $l$ intersects this parabola at points $A$ and $B$, and the midpoint of segment $AB$ is $N(2, \frac{1}{3})$. Find the equation of line $l$.

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