
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
Calculate the following:  
(1) $(-3x^3)^2 - \frac{4x^8}{x^2}$  
(2) $(m-2n)(m+2n) - (m-n)^2$  
(3) When $x=1$, $y=-2$, find the value of the algebraic expression $\left| (3x+y)^2 - y(3x+y) \right| \div (3x)$.

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