
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 a point $M$ on the ellipse $\frac{{{x}^{{2}}}}{{25}}+ \frac{{{y}^{{2}}}{16}}={1}$, let $F\_{{1}}$ and $F\_{{2}}$ be the foci, and $\angle {{F}\_{{1}}}M{{F}\_{{2}}}=\frac{{ }\,{ }\pi }{6}$. Determine the area of $\triangle MF\_{1}F\_{{2}}$.

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