
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 \( X \) be a set of \( n \) points. Let \( P \) be a set of subsets of \( X \), such that if \( A, B \in P \), then \( X - A \), \( A \cup B \), \( A \cap B \in P \). What are the possible values for the number of elements of \( P \)?

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