
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
(1) Given the function $f(x) = |x-1| + |x+3|$, find the range of $x$ for which $f(x)$ is a constant function;  
(2) If $x, y, z \in \mathbb{R}$, and $x^2 + y^2 + z^2 = 1$, find the maximum value of $m = \sqrt{2}x + \sqrt{2}y + \sqrt{5}z$.

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