
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 $f(x)=a^{x}+x^{2}-x\ln a(a > 0,a\neq 1)$.

1. Find the equation of the tangent line to the function $f(x)$ at the point $(0,f(0))$;
2. Find the interval(s) where the function $f(x)$ is strictly increasing;
3. If there exist $x_{1}$, $x_{2}∈[-1,1]$, such that $|f(x_{1})-f(x_{2})|≥e-1(e$ is the base of the natural logarithm$)$, find the range of values for the real number $a$.

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