
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 \( ABC \). On side \( AB \), point \( K \) is marked, and on side \( BC \), points \( L \) and \( M \) are marked (with \( L \) lying on segment \( BM \)) such that \( KL = KM \), \( BL = 2 \), and \( AK = 3 \). Find \( CM \).

![](https://cdn.mathpix.com/cropped/2024_05_06_297c289048f559686628g-33.jpg?height=1069&width=1080&top_left_y=0&top_left_x=0)

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