
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
A sphere touches the edges \( AS, BS, BC \), and \( AC \) of the triangular pyramid \( SABC \) at points \( K, L, M \), and \( N \) respectively.

Find the segment \( KL \) if \( MN = 7 \), \( NK = 5 \), \( LN = 2\sqrt{29} \), and \( KL = LM \).

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