
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
Let $a_1, a_2, \dots, a_{2018}$ be the roots of the polynomial
\[ x^{2018} + 2x^{2017} + \dots + 3x^2 + 4x - 2000 = 0. \]
Compute
\[ \sum_{n = 1}^{2018} \frac{1}{1 - a_n}. \]

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