
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 $f(x)=e^{x}-ax+e^{2}-7$.  
$(1)$ When $a=2$, find the equation of the tangent line to the curve $y=f(x)$ at $x=2$.  
$(2)$ If for any $x\geq 0$, $f(x)\geq \frac{7}{4}x^2$ always holds, find the range of values for $a$.

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