
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 universal set U = R, set A = {x | x^2 - 2x - 3 > 0, x ∈ R}, set B = {x | m - 2 ≤ x ≤ m + 2}, and set C = {x ∈ Z | 8 < 2^(x+2) ≤ 64}.
(1) Find A ∪ C;
(2) If (∁\_UA) ∩ B = {x | 0 ≤ x ≤ 3}, find the value of the real number m.

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