
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 $A=\{a|x^2+2ax+4>0 \text{ holds for all } x \in \mathbb{R}\}$, and $$B=\{x|1< \frac{x+k}{2}<2\}$$  
(1) If $k=1$, find $A\cap C_{\mathbb{R}}B$;  
(2) If $C_{\mathbb{R}}A \subsetneq C_{\mathbb{R}}B$, find the range of the real number $k$.

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