
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 universal set $U$, and non-empty subsets $A$ and $B$ of $U$, such that "x∈A" and "x∈B" are a pair of mutually exclusive events, find the total number of groups $U(A, B)$ when the set $U$ is equal to $\{1, 2, 3, 4, 5\}$.

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