
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
On the sides \( AB, BC \), and \( AC \) of triangle \( ABC \), points \( K, L \), and \( M \) are taken respectively, such that \( AK:KB = 2:3 \), \( BL:LC = 1:2 \), and \( CM:MA = 3:1 \). In what ratio does the segment \( KL \) divide the segment \( BM \)?

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