
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 polynomial given by 
\[ x^{10} + x^9 + \dots + x^2 + x - 42 = 0. \]
Let $b_1, b_2, \dots, b_{10}$ be the roots of this polynomial. Compute
\[ \sum_{n=1}^{10} \frac{1}{1 + b_n}. \]

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