
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) $a^3-9a$  
(2) $3x^2-6xy+x$  
(3) $n^2(m-2)+n(2-m)$  
(4) $-4x^2+4xy+y^2$  
(5) $a^2+2a-8$

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