
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 $U = \{x \in \mathbb{Z} | 0 < x \leq 10\}$, $A = \{1, 2, 4, 5, 9\}$, $B = \{4, 6, 7, 8, 10\}$, and $C = \{3, 5, 7\}$. Find $A \cap B$, $A \cup B$, $(\complement_U A) \cap (\complement_U B)$, $(\complement_U A) \cup (\complement_U B)$, $(A \cap B) \cap C$, and $(A \cup B) \cap C$.

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