
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 $U = \mathbb{R}$, and let the set $A = \{x \in \mathbb{R} | x^2 - 2x - 3 > 0\}$ and set $B = \{x \in \mathbb{R} | |x - a| > 3\}$. Find the complement of set A in U, denoted by $\complement_U A$. If the intersection of $\complement_U A$ and B is an empty set, then determine the range of the real number $a$.

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