
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
Consider $x^2 + px + q=0$, where $p$ and $q$ are positive numbers. If the square of the difference between the roots of this equation is equal to 9, then what is the value of $p$?
A) $\sqrt{4q + 1}$
B) $\sqrt{4q + 9}$
C) $\sqrt{4q - 9}$
D) $\sqrt{4q + 4}$

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