
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 triangle \(ABC\) with sides \(AB = 13\), \(BC = 14\), and \(AC = 15\). Point \(K\) is marked on side \(AB\), point \(L\) is marked on side \(BC\), and point \(N\) is marked on side \(AC\). It is known that \(BK = \frac{14}{13}\), \(AN = 10\), and \(BL = 1\). A line is drawn through point \(N\) parallel to \(KL\) which intersects side \(BC\) at point \(M\). Find the area of the quadrilateral \(KLMN\).

Answer: \(\frac{36503}{1183}=30 \frac{1013}{1183}\).

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