
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 $(a, b, c, d)$ of nonnegative real numbers such that
\begin{align*}
a^2 + b^2 + c^2 + d^2 &= 4 \\
a^5 + b^5 + c^5 + d^5 &= 4.
\end{align*}

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