
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
Given the function $f(x) = ax^2 + bx + c$ ($a \neq 0$), let the set of zeros of the function $y = [f(x)]^2 + pf(x) + q$ be denoted as $A$. Which of the following sets cannot be the set $A$?  
① $\{ \sqrt {2}, \sqrt {3}\}$  
② $\{ \frac {1}{2}, \frac {1}{3}, \frac {1}{4}\}$  
③ $\{-2, 3, 8\}$  
④ $\{-4, -1, 0, 2\}$  
⑤ $\{1, 3, 5, 7\}$．

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