
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 $200i \leq n < 200(i + 1)$. For example, $S_4'$ is the set ${800, 801, 802, \ldots, 999}$. Determine how many of the sets $S_0', S_1', S_2', \ldots, S_{499}'$ do not contain a perfect square?

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