
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
Simplify the following fraction as much as possible:

$$
\frac{16 x^{4} z^{4}-x^{4} y^{16}-64 x^{4} y^{2} z^{4}+4 x^{4} y^{18}+32 x^{2} y z^{4}-2 x^{2} y^{17}+16 y^{2} z^{4}-y^{18}}{\left(2 x^{2} y-x^{2}-y\right)\left(8 z^{3}+2 y^{8} z+4 y^{4} z^{2}+y^{12}\right)\left(2 z-y^{4}\right)}
$$

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