
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 that $A$ and $B$ are two subsets of the set $\{1, 2, 3, \cdots, 100\}$, satisfying that the number of elements in $A$ is equal to the number of elements in $B$ and $A \cap B = \emptyset$. Additionally, for each $n \in A$, it is required that $2n + 2 \in B$. Determine the maximum number of elements in the set $A \cup B$.

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