
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 the roots of the equation

\[ 1 - \frac{x}{1} + \frac{x(x-1)}{2!} - \frac{x(x-1)(x-2)}{3!} + \frac{x(x-1)(x-2)(x-3)}{4!} - \frac{x(x-1)(x-2)(x-3)(x-4)}{5!} + \frac{x(x-1)(x-2)(x-3)(x-4)(x-5)}{6!} = 0 \]

(Where \( n! = 1 \cdot 2 \cdot 3 \cdots n \))

In the answer, specify the sum of the found roots.

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