
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 a triangle \( ABC \) where \( AB = 15 \text{ cm} \), \( BC = 12 \text{ cm} \), and \( AC = 18 \text{ cm} \). In what ratio does the center of the inscribed circle divide the angle bisector of \( \angle C \)?

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