
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  $N$  satisfy all of the following three conditions?
(i)  $N$  is divisible by  $2020$ .
(ii)  $N$  has at most  $2020$  decimal digits.
(iii) The decimal digits of  $N$  are a string of consecutive ones followed by a string of consecutive zeros.

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