
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
There are unique integers $b_{2},b_{3},b_{4},b_{5},b_{6},b_{7},b_{8}$ such that
\[\frac {5}{8} = \frac {b_{2}}{2!} + \frac {b_{3}}{3!} + \frac {b_{4}}{4!} + \frac {b_{5}}{5!} + \frac {b_{6}}{6!} + \frac {b_{7}}{7!} + \frac {b_{8}}{8!},\]
where $0\leq b_{i} < i$ for $i = 2,3,\ldots,8$. Find $b_{2} + b_{3} + b_{4} + b_{5} + b_{6} + b_{7} + b_{8}$.
A) 4
B) 5
C) 6
D) 7
E) 8

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