
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 a right triangle \(ABC\) with legs \(AB = 10\) and \(AC = 24\), medians \(AM\) and \(CN\) are drawn, where \(M\) and \(N\) are the midpoints of the sides \(BC\) and \(AB\), respectively. Point \(I\) lies on the 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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