
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 set $S=\{1,2\}$. $A$ and $B$ are two subsets of $S$. If $A \cup B = S$, then $(A, B)$ is called a partition of the set $S$, if and only if $A=B$, $(A, B)$ and $(B, A)$ are considered the same partition. How many different partitions of the set $S$ are there?

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