
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 circle passing through the vertex $A$ of triangle $ABC$ is tangent to side $BC$ at point $M$ and intersects sides $AC$ and $AB$ respectively at points $L$ and $K$, different from vertex $A$. Find the ratio $AC: AB$, given that the length of segment $LC$ is twice the length of segment $KB$, and the ratio $CM: BM = 3: 2$.

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