
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
If the distinct numbers \( a, b, \) and \( c \) satisfy the following equations:

$$
\begin{aligned}
& a^{3} + p a + q = 0 \\
& b^{3} + p b + q = 0 \\
& c^{3} + p c + q = 0
\end{aligned}
$$

then

$$
a + b + c = 0
$$

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