
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 two triangles, where the sides of the first triangle are 8 cm, 18 cm, and 12 cm, and the sides of the second smaller triangle are 4 cm, 9 cm, and 6 cm. The angle between the first two sides of both triangles is $120^\circ$. Find the length of the segment corresponding to the 12 cm side in the smaller triangle.

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