
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) = |x-2| - m (x ∈ R), and the solution set of f(x+2) ≤ 0 is [-1, 1].
(1) Find the value of the real number m;
(2) Suppose a, b, c ∈ R^+, and a^2 + b^2 + c^2 = m, find the maximum value of a + 2b + 3c.

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