
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
In the triangular prism \(A B C A_{1} B_{1} C_{1}\), two sections are made. The first section passes through edge \(A B\) and the midpoint of edge \(C C_{1}\), and the second section passes through edge \(A_{1} B_{1}\) and the midpoint of edge \(C B\). Find the ratio of the length of the segment of the intersection line of these sections, contained within the prism, to the length of edge \(A B\).

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