
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:  
(1) $x^2y-4xy+4y$  
(2) $9(a+b)^2-(a-b)^2$  
(3) $12a^2b-18ab^2-24a^3b^3$  
(4) $4a(x-2)^2-2b(2-x)^3$  
(5) $a(a-2b)(2a-3b)-2b(2b-a)(3b-2a)$

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