
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
Let  $N$  be the smallest positive integer such that  $N+2N+3N+\ldots +9N$  is a number all of whose digits are equal. What is the sum of digits of  $N$ ?

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