
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
An isosceles triangle with sides \( AB = BC = 3 \) and \( AC = 4 \) has an inscribed circle, which touches the sides of the triangle at points \( K, L \), and \( M \). Find the ratio of the areas \( S(\triangle ABC) : S(\triangle KLM) \).

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