
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
If the function $y = x^2 + px + q + ax^2$ has a minimum value of zero, and $a$ is a positive constant, what is the value of $q$?
A) $\frac{p^2}{4}$  
B) $\frac{p^2}{2(1+a)}$  
C) $\frac{p^2}{4(1+a)}$  
D) $\frac{-p^2}{4(1+a)}$  
E) $\frac{p^2}{2 + a}$

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