
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 the function $y = x^2 + 3px + 2p^2$, where $p$ is a positive constant. Determine the $x$-value at which this function attains its minimum value.
**A**. $x = -\frac{p}{2}$  
**B**. $x = -p$  
**C**. $x = -\frac{3p}{2}$  
**D**. $x = -2p$  
**E**. $x = -3p$

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