
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 with sides 12 cm, 15 cm, and 18 cm. A circle is drawn that touches both of the shorter sides and has its center on the longest side. Find the segments into which the center of the circle divides the longest side of the triangle.

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