
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 $f(x) = 1 + x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \ldots + \frac{x^{2015}}{2015}$; $g(x) = 1 - x + \frac{x^2}{2} - \frac{x^3}{3} + \frac{x^4}{4} - \ldots - \frac{x^{2015}}{2015}$; let the function $F(x) = [f(x+3)] \cdot [g(x-4)]$, and all zeros of the function $F(x)$ are within the interval $[a, b]$ ($a < b$, $a, b \in \mathbb{Z}$), find the minimum value of $b-a$.

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