
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) $6(x-3)^2-24$
(2) $(a-2b)^2-(2a+b)^2$
(3) $3p(x+1)^3y^2+6p(x+1)^2y+3p(x+1)$

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