
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
(15 points) Let $A = \{x | x \text{ is a positive integer less than } 9\}$, $B = \{1, 2, 3\}$, and $C = \{3, 4, 5, 6\}$. Find $A \cap B$, $A \cap C$, $A \cap (B \cup C)$, and $A \cup (B \cap C)$.

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