
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 an ellipse $\frac{x^{2}}{24} + \frac{y^{2}}{12} = 1$ and a point $M(3,1)$ within it, a line $l$ is drawn through $M$ intersecting the ellipse at points $A$ and $B$.

(I) If $AB$ is bisected by point $M$, find the equation of line $l$.
(II) If the angle of inclination of line $l$ is $\frac{\pi}{4}$, find $|AB|$.

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