
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 set \( A = \{1, 2, 3\} \), find the total number of different pairs of subsets \([A_1, A_2]\) that are considered a bipartite set partition of \( A \), where \( A_1 \cup A_2 = A \) and \([A_1, A_2]\) is considered the same as \([A_2, A_1]\).

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