
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 $f(x)=(x+a)e^{x}$, where $a\in \mathbb{R}$.  
$(1)$ When $a=1$, find the equation of the tangent line to the graph of $f(x)$ at the point $\left(0,f(0)\right)$.  
$(2)$ For any $x\in \mathbb{R}$, if the inequality $f(x) \geq \frac{1}{6}x^3-x-2$ always holds, find the range of values for $a$.

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