
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 \(ABC\), whose area is \(S\), the side lengths \(AB\) and \(AC\) are in the ratio \(1:5\). The midline parallel to \(BC\) intersects the median and bisector drawn from point \(A\) at points \(M\) and \(N\) respectively. Find the area of triangle \(AMN\).

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