
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 every positive integer  $n$ , form the number  $n/s(n)$ , where  $s(n)$  is the sum of digits of  $n$  in base 10. Determine the minimum value of  $n/s(n)$  in each of the following cases:

(i)  $10 \leq n \leq 99$ 
(ii)  $100 \leq n \leq 999$ 
(iii)  $1000 \leq n \leq 9999$ 
(iv)  $10000 \leq n \leq 99999$ 

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