
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 $f(x)=e^{x}-x$ where $e$ is the base of the natural logarithm.

(1) Find the equation of the tangent line to the curve $y=f(x)$ at the point $(-\ln 2,f(-\ln 2))$;

(2) Find the range of values of the real number $a$ such that the inequality $f(x) > ax$ always holds when $x\in[0,2]$;

(3) Let $g(x)=f(x)-ax$. Find the range of values of the real number $a$ such that the function $g(x)$ has exactly one zero point.

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