
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 passing through the vertex \( A \) of triangle \( ABC \) perpendicular to its median \( BD \) bisects this median.

Find the ratio of the sides \( AB \) and \( AC \).

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