
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
On a blackboard, there are 1989 consecutive natural numbers written from $1, 2, 3, \ldots, 1989$. A transformation is performed as follows: erase any two numbers on the blackboard and replace them with the remainder when the sum of the two erased numbers is divided by 19. After performing this transformation multiple times, there are two numbers left on the blackboard: one is 89 and the other is a single-digit number. What is this single-digit number?

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