
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 distinct integers $b_{2},b_{3},b_{4},b_{5},b_{6},b_{7},b_{8},b_{9}$ such that
\[
\frac{7}{11} = \frac{b_{2}}{2!} + \frac{b_{3}}{3!} + \frac{b_{4}}{4!} + \frac{b_{5}}{5!} + \frac{b_{6}}{6!} + \frac{b_{7}}{7!} + \frac{b_{8}}{8!} + \frac{b_{9}}{9!}
\]
where $0 \leq b_i < i$ for $i = 2,3,\ldots,9$. Find $b_{2} + b_{3} + b_{4} + b_{5} + b_{6} + b_{7} + b_{8} + b_{9}$.
A) 14
B) 15
C) 16
D) 17
E) 18

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