
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
If sets $A_1$ and $A_2$ satisfy $A_1 \cup A_2 = A$, then $(A_1, A_2)$ is called a partition of set $A$, and it is defined that: $(A_1, A_2)$ and $(A_2, A_1)$ are considered the same partition of set $A$ if and only if $A_1 = A_2$. The number of different partitions of the set $A=\{a_1, a_2, a_3\}$ is ______.

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