
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
Consider sets A and B, where $A=\{x|y=\log_{2}(x-1)\}$ and $B=\{y|y=-x^{2}+2x-2, x \in \mathbb{R}\}$.
(1) Find the sets A and B.
(2) Let set C be $C=\{x|2x+a<0\}$. If $B \cup C = C$, determine the range of the real number $a$.

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