
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
\[
p + q + r + s = 8,
\]
\[
p^2 + q^2 + r^2 + s^2 = 16.
\]
Let \( m \) and \( M \) denote the minimum and maximum values of
\[
(p^3 + q^3 + r^3 + s^3) - 2(p^2 + q^2 + r^2 + s^2).
\]
Find \( m + M \).

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