
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 ellipse $C: \frac{x^2}{16} + \frac{y^2}{12} = 1$ with foci $F_1$ and $F_2$, find the largest angle in $\triangle F_1MF_2$ for a point $M$ that lies on $C$ and satisfies $|MF_1| - |MF_2| = 2$.

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