
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
Given an equilateral triangle \( KLM \) with a side length of \(\frac{1}{4}\) located inside (or on the boundary of) an equilateral triangle \( ABC \) with a side length of 1, find the distances from point \( A \) to the lines \( KL \), \( LM \), and \( MK \), and determine the position of triangle \( KLM \) when these distances are minimal.

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