
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
How many positive integers  $N$  in the segment  $\left[10, 10^{20} \right]$  are such that if all their digits are increased by  $1$  and then multiplied, the result is  $N+1$ ?

*(F. Bakharev)*

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