
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
Through the points \( A(0 ; 14) \) and \( B(0 ; 4) \) two parallel lines are drawn. The first line, passing through point \( A \), intersects the hyperbola \( y = \frac{1}{x} \) at points \( K \) and \( L \). The second line, passing through point \( B \), intersects the hyperbola \( y = \frac{1}{x} \) at points \( M \) and \( N \).

What is the value of \( \frac{A L - A K}{B N - B M} \)?

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