
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 the 1992 Japan Mathematical Olympiad, consider points \( P, Q, R \) on the sides \( BC, CA, AB \) of triangle \( \triangle ABC \) such that these points divide the sides in the ratio \( t:(1-t) \). The area of the triangle formed by line segments \( AP, BQ, CR \) is \( K \), and the area of \( \triangle ABC \) is \( L \). Find the ratio \(\frac{K}{L}\) in terms of \( t \).

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