
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  $n$ , let  $s(n)$  be the sum of the digits of  $n$ . Find the smallest positive integer  $k$  such that
\[s(k) = s(2k) = s(3k) = \cdots = s(2013k) = s(2014k).\]

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