
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
In triangle $\mathrm{ABC}$, the sides are $\mathrm{AB}=10$, $\mathrm{AC}=24$, and $\mathrm{BC}=26$. Medians $\mathrm{AM}$ and $\mathrm{CN}$ are drawn, with $\mathrm{M}$ and $\mathrm{N}$ being the midpoints of the sides $\mathrm{BC}$ and $\mathrm{AB}$, respectively. Point I lies on side $\mathrm{AC}$, and $\mathrm{BI}$ is the angle bisector. Find the area of triangle $\mathrm{MNI}$.

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