
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 functions $f(x)=e^{x}$ and $g(x)=a(x^{2}-x)$ where $a\in \mathbb{R}$.  
$(1)$ When $a=-1$, find the equations of the tangent lines to $f(x)$ and $g(x)$ passing through the point $(0,0)$.  
$(2)$ If $f(x)+g(x)-\cos x\geqslant 0$, find the range of values for $a$.

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