
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 equation \(1 + x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \cdots - \frac{x^{2018}}{2018} = 0\) with all real roots within the interval \([a, b]\), where \(a\) and \(b\) are integers such that \(a < b\), calculate the minimum value of \(b - a\).

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