
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
$(1)$ Calculate: $(-8ab) \cdot (\frac{3}{4}a^2b)$;  
$(2)$ Calculate: $2022^{2} - 2020 \times 2024$ (simplify the calculation);  
$(3)$ Calculate: $(15x^{2}y - 10xy^{2}) \div 5xy$;  
$(4)$ Calculate: $(2x+3y)^{2} - (2x+y)(2x-y)$;  
$(5)$ Factorize: $(x+m)^{2} - (x+n)^{2}$;  
$(6)$ Factorize: $3ax^{2} + 6axy + 3ay^{2}$.

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