
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
For any integer  $n \ge 2$ , let  $b_n$  be the least positive integer such that, for any integer  $N$ ,  $m$  divides  $N$  whenever  $m$  divides the digit sum of  $N$  written in base  $b_n$ , for  $2 \le  m \le n$ . Find the integer nearest to  $b_{36}/b_{25}$ .

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