
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 $y= \sqrt {4-2^{x}}$, its domain is $A$, and the range of the function $y= \lg (x-1) (x \in [2,11])$ is $B$.

1. Find $A$ and $B$.
2. Find $(C_{R}A) \cup B$.

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