
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 \( \triangle ABC \), points \( P \), \( Q \), and \( R \) divide the sides \( BC \), \( CA \), and \( AB \) in the ratio \( t:(1-t) \) respectively. Let \( K \) be the area of the triangle formed by the segments \( AP \), \( BQ \), and \( CR \), and \( L \) be the area of \( \triangle ABC \). Find \( \frac{K}{L} \) in terms of \( t \).

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