
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

The decimal representation of a natural number \( N \) contains 1580 digits. Among these digits, there are threes, fives, and sevens, and there are no other digits. It is known that the number of sevens is 20 less than the number of threes. Find the remainder when \( N \) is divided by 3.

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