
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
Consider the roots \( b_1, b_2, \dots, b_{1009} \) of the polynomial
\[ x^{1009} + x^{1008} + x^{1007} + \dots + x^2 + x - 671 = 0. \]
Calculate the sum:
\[ \sum_{n = 1}^{1009} \frac{1}{1 - b_n}. \]

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