
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
(1) Factorize: $2a^3 - 12a^2 + 8a$  
(2) Calculate: $\frac{3}{a} - \frac{6}{1-a} - \frac{a+5}{a^2-a}$  
(3) Solve the equation: $\frac{x-2}{x+2} - \frac{12}{x^2-4} = 1$.

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