
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 sets \( A \) and \( B \) are subsets of the universal set \( U = \{1, 2, 3, 4\} \), and the following conditions are satisfied:
- \( \left.\complement_{U} A\right) \cap B = \{1\} \)
- \( A \cap B = \{3\} \)
- \( \left(\complement_{U} A\right) \cap \left(\complement_{U} B\right) = \{2\} \)

Find \( \complement_{U}(A \cup B) \).

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