
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
Given the function $f(x) = m - |x - 2|$, where $m \in \mathbb{R}$, and the solution set of $f(x + 2) \geq 0$ is $[-1, 1]$.

(1) Find the value of $m$;  
(2) If $a, b, c \in \mathbb{R}_+$, and $\frac{1}{a} + \frac{1}{2b} + \frac{1}{3c} = m$, find the minimum value of $Z = a + 2b + 3c$.

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