
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 the ends of the major axis of the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{7} = 1$ are the foci of the hyperbola $E$, and the eccentricity of the hyperbola $E$ is $\frac{3}{2}$.

(I) Find the standard equation of the hyperbola $E$;

(II) If a line $l$ with a slope of $1$ intersects the hyperbola $E$ at points $A$ and $B$, and the $x$-coordinate of the midpoint of segment $AB$ is $4\sqrt{2}$, find the equation of line $l$.

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