
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

Let $t = \log_{x^{2019}} 2018$. Then the equation takes the form: $t + t^{2} + t^{3} + \ldots = 2018$.

Simplifying the left-hand side of the last equation using the sum formula for an infinite decreasing geometric series, we get: $\frac{t}{1-t} = 2018$.

From this, $t = \frac{2018}{2019}$.

We obtain $\log_{x^{2019}} 2018 = \frac{2018}{2019}$, and $\left(x^{2019}\right)^{\frac{2018}{2019}} = 2018$, so $x = \sqrt[2018]{2018}$.

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