
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 set A = $\{x \in \mathbb{R} \mid 0 \leq \log_2 x \leq 2\}$.
(i) If set B = $\{a^2+4a+8, a+3, 3\log_2 |-a|\}$ and it satisfies B $\subseteq$ A, find the value of the real number a;
(ii) If set C = $\{y \mid y = x^m, x \in A, m \in \mathbb{R}\}$ and it satisfies A $\cup$ C = A, find the range of the real number m.

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