
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 $T_i$ be the set of all integers $n$ such that $200i \leq n < 200(i + 1)$. Determine how many of the sets $T_0, T_1, T_2, \ldots, T_{499}$ do not contain a perfect square.

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