
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 \( ABC \), a line through the foot \( D \) of altitude \( BD \) is drawn parallel to side \( AB \) and intersects side \( BC \) at point \( K \). Find the ratio \(\frac{BK}{KC}\) if the area of triangle \( BDK \) is \(\frac{3}{16}\) of the area of triangle \( ABC \).

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