
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 $U = \{x \mid x$ is a prime number not exceeding 20 $\}$. If $A \cap \complement_{U} B = \{3, 5\}$, $\complement_{U} A \cap B = \{7, 19\}$, and $\complement_{U}(A \cup B) = \{2, 17\}$, find the sets $A$ and $B$.

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