
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 $F_{1}$ and $F_{2}$ be two foci of ellipse $C$, $M$ be a point on ellipse $C$, $|MF_{1}|=12$, $|MF_{2}|=16$, $sin∠M{F_2}{F_1}=\frac{3}{5}$. Find the eccentricity $e$ of ellipse $C$.

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