
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
Points \( C_{1} \), \( B_{1} \), and \( A_{1} \) are located on the sides \( AB \), \( AC \), and \( BC \) respectively of an equilateral triangle \( ABC \), such that the triangle \( A_{1} B_{1} C_{1} \) is also equilateral. The altitude \( BD \) of triangle \( ABC \) intersects the side \( A_{1} C_{1} \) at point \( O \). Find the ratio \( \frac{BO}{BD} \) if \( \frac{A_{1}B_{1}}{AB} = n \).

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