
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
Let $x_1$, $x_2$, and $x_3$ be distinct real numbers such that they are roots of the cubic equation $2x^3 - px^2 + qx - d = 0$. If $p, q, d$ are positive numbers and $q = 2d$, find $x_1 + x_2 + x_3$.
A) $\frac{p}{2}$  
B) $\frac{2d}{3}$  
C) $\frac{q}{2}$  
D) $p$

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