
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 \( 150i \leq n < 150(i + 1) \). For example, \( S_4 \) is the set \{600, 601, 602, \ldots, 749\}. How many of the sets \( S_0, S_1, S_2, \ldots, S_{666} \) do not contain a perfect square?

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