
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
Given the functions $f(x)=1+x- \frac{x^{2}}{2}+ \frac{x^{3}}{3}- \frac{x^{4}}{4}+…+ \frac{x^{2017}}{2017}$ and $g(x)=1-x+ \frac{x^{2}}{2}- \frac{x^{3}}{3}+ \frac{x^{4}}{4}-…- \frac{x^{2017}}{2017}$, define the function $F(x)=f(x+4) \cdot g(x-5)$. Find the minimum value of the difference between the upper and lower bounds, $b-a$, of the interval that contains all the zeros of the function $F(x)$, where $a, b \in \mathbb{Z}$ and $a < b$.

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