
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
There are two similar triangles on the plane, each with a distinct set of side lengths given in centimeters. The larger triangle has side lengths of $16$ cm, $20$ cm, and $24$ cm, and the angle opposite the shortest side ($16$ cm) is $30^\circ$. The smaller triangle has side lengths of $8$ cm and $12$ cm, with the third side being $AB$. Calculate the length of the segment $AB$.

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