
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
We say that a positive real number  $d$  is  $good$  if there exists an infinite squence  $a_1,a_2,a_3,...\in (0,d)$  such that for each  $n$ , the points  $a_1,a_2,...,a_n$  partition the interval  $[0,d]$  into segments of length at most  $\frac{1}{n}$  each . Find  $\text{sup}\{d| d  \text{is  good}\}$ .

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