
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 triples $(a,b,c)$ of nonnegative real numbers such that:
\begin{align*}
a^2 + b^2 + c^2 &= 3, \\
(a + b + c)(a^2b + b^2c + c^2a) &= 9.
\end{align*}

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