
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 the universal set $U=\{a_{1},a_{2},a_{3},a_{4}\}$, the set $A$ is a subset of $U$ with exactly two elements, and satisfies the following three conditions:
1. If $a_{1} \in A$, then $a_{2} \in A$;
2. If $a_{3} \notin A$, then $a_{2} \notin A$;
3. If $a_{3} \in A$, then $a_{4} \notin A$.

Then, the set $A=$ ______. (Express using the enumeration method)

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