
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 scouting team has a 255.3 m rope and needs to delineate a pentagon, which is divided by one of its diagonals into a rectangle and an isosceles right triangle, and has the largest possible area. Some suggest the diagonal should be 66 m, while others suggest it should be 67 m. Which suggestion is better? Could there be an even better suggestion?

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