
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 \(ABC\), the sides are \(AB = 10\), \(AC = 24\), and \(BC = 26\). The medians \(AM\) and \(CN\) are drawn, where points \(M\) and \(N\) are the midpoints of sides \(BC\) and \(AB\), respectively. Point \(I\) lies on side \(AC\), and \(BI\) is the angle bisector. Find the area of triangle \(MNI\).

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