
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 a regular triangular pyramid \( SKLM \) with vertex \( S \), a median \( MP \) is drawn in triangle \( SLM \). It is known that \( KL = 1 \) and \( SK = 3 \). Through the midpoint \( N \) of edge \( SM \), a line \( NE \) is drawn parallel to \( KL \). Through point \( K \), a line is drawn that intersects lines \( MP \) and \( NE \) at points \( A \) and \( B \) respectively. Find \( AB \).

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