
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 set $A=\{x\in \mathbb{R} | 0 \leq \log_{2}x \leq 2\}$.
- (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 $C=\{y | y=x^{m}, x\in A, m\in \mathbb{R}\}$, 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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