
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 solutions \((x_{1}, x_{2}, \ldots, x_{n})\) of the equation
$$
1+\frac{1}{x_{1}}+\frac{x_{1}+1}{x_{1} x_{2}}+\frac{\left(x_{1}+1\right)\left(x_{2}+1\right)}{x_{1} x_{2} x_{3}}+\cdots+\frac{\left(x_{1}+1\right) \cdots\left(x_{n-1}+1\right)}{x_{1} x_{2} \cdots x_{n}}=0
$$

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