
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 square with a side of 20 cm is given. It is divided into two groups of equal segments, one group with three segments and the other with four segments. What are the lengths of these segments? Find all possible answers.

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