
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 \( \triangle ABC \), \( BD \) is a median, point \( P \) lies on \( BD \) with the ratio \( |BP| : |PD| = 3:1 \), and \( AP \) intersects \( BC \) at \( K \). Find the ratio of the area of \( \triangle ABK \) to the area of \( \triangle ACK \).

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