
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
Let $U=\{x \in \mathbb{Z} | 0 < x \leq 10\}$, $A=\{1, 2, 4, 5, 9\}$, $B=\{4, 6, 7, 8, 10\}$. Find $A \cap B$, $A \cup B$, $\complement_U (A \cup B)$, and $(\complement_U A) \cap (\complement_U B)$.

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