
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 \( A B C \), a median \( B M \) is drawn. In triangle \( A B M \), a median \( B N \) is drawn. In triangle \( B N C \), a median \( N K \) is drawn. It turns out that \( N K \perp B M \). Find \( \frac{A B}{A C} \).

Answer: \( \frac{1}{2} \)

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