
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 \(a_1, a_2, \dots, a_{1000}\) be the roots of the polynomial
\[
x^{1000} + x^{999} + \dots + x^2 + x + 1789 = 0.
\]
Compute
\[
\sum_{n=1}^{1000} \frac{1}{2-a_n},
\]
where \(a_n \neq 2\) for all \(n\).

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