
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 $A=\{x|x \text{ satisfies condition } p\}$, $B=\{x|x \text{ satisfies condition } q\}$ (fill in the number)  
If $A \subseteq B$, then $p$ is a ______ condition for $q$;  
If $B \subseteq A$, then $p$ is a ______ condition for $q$;  
If $A = B$, then $p$ is a ______ condition for $q$.  
① Sufficient condition      ② Necessary condition  
③ Necessary and sufficient condition      ④ Neither sufficient nor necessary condition.

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