
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 \(\alpha_{1}, \alpha_{2}, \alpha_{3}\) be the three roots of the equation \(5 x^{3} - 6 x^{2} + 78 + 8 = 0\). Calculate: \(\left(\alpha_{1}^{2} + \alpha_{1} \alpha_{2} + \alpha_{2}^{2} \right)\left(\alpha_{2}^{2} + \alpha_{2} \alpha_{3} + \alpha_{3}^{2}\right)\left(\alpha_{1}^{2} + \alpha_{1} \alpha_{3} + \alpha_{3}^{2}\right)\).

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