
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
Points \( D \) and \( E \) are located on the diagonals \( A B_{1} \) and \( C A_{1} \) of the lateral faces of the prism \( A B C A_{1} B_{1} C_{1} \) such that the lines \( D E \) and \( B C_{1} \) are parallel. Find the ratio of the segments \( D E \) and \( B C_{1} \).

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