
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
Find all non-zero arrays \((x, y, z, w)\) that satisfy
$$
1+\frac{1}{x}+\frac{2(x+1)}{xy}+\frac{3(x+1)(y+2)}{xyz}+\frac{4(x+1)(y+2)(z+3)}{xyzw}=0.
$$

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