
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
(1) Let $A=\{x\in\mathbb{Z} \mid |x|\leq 6\}$, $B=\{1, 2, 3\}$, $C=\{3, 4, 5, 6\}$. Find:  
① $A\cap(B\cap C)$;  
② $A\cap \complement_A(B\cup C)$.  
(2) Calculate: $\lg 25 + \lg 2 \cdot \lg 50 + (\lg 2)^2$.

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