
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 side of a triangle is divided into five equal parts; lines are drawn through the division points parallel to the base.

Find the lengths of the segments of these lines that are enclosed between the other two sides of the triangle, given that the base is 20 units long.

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