
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 each positive integer  $k$ , let  $S(k)$   be the sum of its digits. For example,  $S(21) = 3$  and  $S(105) = 6$ . Let  $n$  be the smallest integer for which  $S(n) - S(5n) = 2013$ . Determine the number of digits in  $n$ .

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