
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 $f(x)=a^{x}+x^{2}-x\ln a$ ($a > 0, a \neq 1$), if there exist $x_{1}, x_{2} \in [-1,1]$ such that $|f(x_{1})-f(x_{2})| \geqslant e-1$ (where $e$ is the base of the natural logarithm), then the range of the real number $a$ is __________.

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