
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 an isosceles triangle $ABC$ with base $AB$ measuring $10 \text{ cm}$ and legs measuring $20 \text{ cm}$ each. Point $S$ is the midpoint of the base $AB$. Divide the triangle $ABC$ into five parts with equal area using four lines passing through point $S$. Determine the lengths of the segments cut by these lines on the legs of the triangle $ABC$.

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