
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 the roots of the cubic equation $3x^3 + 2x^2 + 4x + 1 = 0$ be $r$, $s$, and $t$. Evaluate the sum of the squares of the reciprocals of the roots, i.e., $\alpha^2 + \beta^2 + \gamma^2$ where $\alpha = \frac{1}{r}$, $\beta = \frac{1}{s}$, $\gamma = \frac{1}{t}$.

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