
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
Let the universal set be the set of real numbers $\mathbb{R}$, and let set $A = \{x | x(x-3) < 0\}$, $B = \{x | x \geq a\}$.
1. When $a=1$, find $\complement_{\mathbb{R}}(A \cup B)$;
2. If $A \cap B \neq \emptyset$, find the range of the real number $a$.

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