
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 $f(x) = e^{2018x} + mx^3 - m$ $(m > 0)$, when $x_1 + x_2 = 1$, for any real number $\theta$, the inequality $f(x_1) + f(\sin^2 \theta) > f(x_2) + f(\cos^2 \theta)$ always holds, determine the range of the real number $x_{1}$.

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