
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 positive integer  $n$  denote  $S(n)$  the digital sum of  $n$  when represented in the decimal system. Find every positive integer  $M$  for which  $S(Mk)=S(M)$  holds for all integers  $1\le k\le M$ .

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