
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
From any point \( P \) on the line \( l: \frac{x}{12} + \frac{y}{8} = 1 \), draw tangent lines \( PA \) and \( PB \) to the ellipse \( C: \frac{x^{2}}{24} + \frac{y^{2}}{16} = 1 \). The tangent points are \( A \) and \( B \), respectively. Find the trajectory of the midpoint \( M \) of the line segment \( AB \).

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