
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
Suppose that the roots of $x^3 + 4x^2 + 5x - 14 = 0$ are $\alpha$, $\beta$, and $\gamma$. Assume that the roots of another polynomial $x^3 + px^2 + qx + r = 0$ are $\alpha+\beta$, $\beta+\gamma$, and $\gamma+\alpha$. Find the value of $r$.

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