
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 function $f(x) = 1 + x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \ldots + \frac{x^{2015}}{2015}$, and $g(x) = 1 - x + \frac{x^2}{2} - \frac{x^3}{3} + \frac{x^4}{4} + \ldots - \frac{x^{2015}}{2015}$. Let the function $F(x) = f(x+3) \cdot g(x-4)$, determine the minimum value of $b-a$, where $a$ and $b$ are the endpoints of the interval containing all the zeros of the function $F(x)$, both endpoints being integers.

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