
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 that the universal set $U=\mathbb{R}$, the set $A=\{x \mid 0 < 2x+4 < 10\}$, $B=\{x \mid x < -4 \text{ or } x > 2\}$, and $C=\{x \mid x^2 - 4ax + 3a^2 < 0, a < 0\}$,  
(1) Find $A \cup B$;  
(2) If $\complement_U (A \cup B) \subseteq C$, determine the range of the real number $a$.

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