
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
For a non-empty set of real numbers $A$, denote $A^* = \{y | \forall x \in A, y \geq x\}$. Let $M$ and $P$ be non-empty sets of real numbers, satisfying $M \subseteq P$. Consider the following statements:  
① $P^* \subseteq M^*$;  
② $M^* \cap P \neq \emptyset$;  
③ $M \cap P^* = \emptyset$.  
Among these statements, the correct ones are ____. (Write down the numbers of all correct statements)

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