
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
In the math competition from 1993 in Zhejiang, China, the product $32 \cdot 5N$ results in a 1992-digit natural number. In this number, the digits $1, 2, 3, \cdots, 8$ each appear a number of times that is a multiple of 9. If the sum of the digits of $N$ is $N_{1}$, the sum of the digits of $N_{1}$ is $N_{2}$, and the sum of the digits of $N_{2}$ is $N_{3}$, determine the value of $N_{3}$.

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