
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
Using the approximation calculation method of "replacing curves with straight lines," in the vicinity of the tangent point, the tangent line of the function graph can be used to approximate the curve near the tangent point for calculation. Approximate the value of $\sqrt[2019]{e}$, where $e=2.71828\ldots$ is the base of the natural logarithm. (Answer in decimal form, rounded to four decimal places)

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