
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 2-meter long rope is folded in half and then cut at a point chosen uniformly at random along its length. Find the probability that the longer resultant piece is at least y times the length of the shorter piece, for a given value of y.

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