
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
Given the function $f_n(x) = 1 + \frac{x}{1} + \frac{x(x+1)}{1 \times 2} + \frac{x(x+1)(x+2)}{1 \times 2 \times 3} + \ldots + \frac{x(x+1)(x+2)\ldots(x+n-1)}{1 \times 2 \times 3 \times \ldots \times n}$, find the roots of the equation $f_n(x) = 0$.

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