
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
Determine the $x$-value at which the function $3x^2 + px + q$ reaches its minimum, where $p$ and $q$ are positive constants.
A) $x = -\frac{p}{3}$
B) $x = -\frac{p}{6}$
C) $x = -2p$
D) $x = \frac{p}{6}$
E) $x = \frac{p}{3}$

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