
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 \(a_2, a_3, a_4, a_5, a_6, a_7, a_8\) such that
\[
\frac{8}{13} = \frac{a_2}{2!} + \frac{a_3}{3!} + \frac{a_4}{4!} + \frac{a_5}{5!} + \frac{a_6}{6!} + \frac{a_7}{7!} + \frac{a_8}{8!}
\]
where \(0 \leq a_i < i\) for \(i = 2,3,\ldots,8\). Find \(a_2 + a_3 + a_4 + a_5 + a_6 + a_7 + a_8\).
A) 15
B) 17
C) 19
D) 21
E) 23

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