
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
\[
p + q + r + s = 10, \quad p^2 + q^2 + r^2 + s^2 = 20.
\]
Calculate the minimum and maximum values of
\[
3(p^3 + q^3 + r^3 + s^3) - 2(p^4 + q^4 + r^4 + s^4).
\]

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