
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
Let $M$ be a point on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, and $F_1$, $F_2$ be its foci. If $\angle MF_1F_2 = 75^\circ$ and $\angle MF_2F_1 = 15^\circ$, find the eccentricity of the ellipse.

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