
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
A line parallel to leg \(AC\) of right triangle \(ABC\) intersects leg \(BC\) at point \(K\) and the hypotenuse \(AB\) at point \(N\). On leg \(AC\), a point \(M\) is chosen such that \(MK = MN\). Find the ratio \(\frac{AM}{MC}\) if \(\frac{BK}{BC} = 14\).

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