
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 $p,q,r$ be the roots of $x^3 - 6x^2 + 8x - 1 = 0$, and let $t = \sqrt{p} + \sqrt{q} + \sqrt{r}$. Find $t^4 - 12t^2 - 8t$.

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