
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
Divide a rope of length $2m$ into two segments, such that the square of the longer segment's length is equal to the product of the shorter segment's length and the original rope length. Let the length of the longer segment be $x$ meters. Write the equation for this problem.

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