
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 $p,$ $q,$ $r,$ $s$ be real numbers such that
\begin{align*}
p + q + r + s &= 10, \\
p^2 + q^2 + r^2 + s^2 &= 20.
\end{align*}
Find the minimum and maximum values of
\[3(p^3 + q^3 + r^3 + s^3) - (p^4 + q^4 + r^4 + s^4)\]
and compute their sum.

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