
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
Determine the number of ordered quadruples \((a,b,c,d)\) of nonnegative real numbers satisfying:
\[
a^2 + b^2 + c^2 + d^2 = 4,
\]
\[
(a + b + c + d)(a^4 + b^4 + c^4 + d^4) = 32.
\]

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