
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 \( |A| = |B| \) and \( A \cap B = \varnothing \). If \( x \in A \) always implies \( 2x + 2 \in B \), what is the maximum number of elements in the set \( A \cup B \)?

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