
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 \(\{1, 2, \ldots, 100\}\) such that \( |A| = |B| \), \( A \cap B = \emptyset \), and for any \( x \in A \), \( 2x + 2 \in B \). Find the maximum value of \( |A \cup B| \).

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