
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 $I=\{1,2,3,4\}$, and let $A$ and $B$ be subsets of $I$. If $A \cap B = \{2,3\}$, then the pair $(A,B)$ is called an "ideal pair set". How many "ideal pair sets" satisfy this condition? (Note that $(A,B)$ and $(B,A)$ are considered as two different "ideal pair sets").

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