
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
Let  $ S_i$  be the set of all integers  $ n$  such that  $ 100i\leq n < 100(i \plus{} 1)$ .  For example,  $ S_4$  is the set  $ {400,401,402,\ldots,499}$ .  How many of the sets  $ S_0, S_1, S_2, \ldots, S_{999}$  do not contain a perfect square?

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