
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
Given a positive integer \( N \) such that \( N < 10^{2020} \), when 7 is placed at the beginning of \( N \), the resulting number is 5 times the number formed when 7 is placed at the end of \( N \). How many different values \( N \) can take?

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