
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 $A=\{x|x$ is a positive integer less than $11\}$, $B=\{1,2,3,4\}$, and $C=\{3,4,5,6,7\}$. Find:

1. $A\cap C$, $\complement _{A}B$;
2. $\complement _{A}(B\cup C)$, $A\cup (B\cap C)$.

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