
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 $x^2 + px + 2q$ where $p$ and $q$ are positive numbers, at which $x$ value does the function achieve its minimum value?
**A)** $x = -p$  
**B)** $x = \frac{p}{2}$  
**C)** $x = -2p$  
**D)** $x = \frac{p^2}{4q}$  
**E)** $x = \frac{-p}{2}$

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