
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) $ax^2-7ax+6a$  
(2) $xy^2-9x$  
(3) $1-x^2+2xy-y^2$  
(4) $8(x^2-2y^2)-x(7x+y)+xy.$

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