
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
Find the number of ordered quadruples $(p,q,r,s)$ of nonnegative real numbers such that
\[
p^2 + q^2 + r^2 + s^2 = 9,
\]
\[
(p + q + r + s)(p^3 + q^3 + r^3 + s^3) = 81.
\]

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