
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 real numbers such that:
\[
x + y + z = 5, \\
x^2 + y^2 + z^2 = 11.
\]
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}
user