
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 \(x, y, z\) be nonnegative real numbers such that
\begin{align*}
x + y + z &= 3, \\
x^2 + y^2 + z^2 &= 5.
\end{align*}
Let \(m\) and \(M\) be the smallest and largest possible values of \(x\), respectively. Find \(m + M\).

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