
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
Factorize the following expressions:  
(1) $3ax^2+6axy+3ay^2$  
(2) $a^2(x-y)-b^2(x-y)$  
(3) $a^4+3a^2-4$;  
(4) $4x^2-y^2-2y-1$.

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