
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 parallelogram \( KLMN \), side \( KL \) is equal to 8. A circle, tangent to sides \( NK \) and \( NM \), passes through point \( L \) and intersects sides \( KL \) and \( ML \) at points \( C \) and \( D \) respectively. It is known that \( KC : LC = 4 : 5 \) and \( LD : MD = 8 : 1 \). Find the side \( KN \).

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