
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
A right triangle with sides 6 cm, 8 cm, and 10 cm has an inscribed circle. Lines parallel to the sides of the triangle are drawn through the center of the circle. Calculate the lengths of the segments of the sides of the triangle that are cut off by these lines.

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