
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 $f(x) = e^{x} - x^{2} - 1$.  
$(1)$ Determine whether there exist extreme values for $f(x)$ in its domain. If they exist, find the extreme values; if not, explain the reason.  
$(2)$ If $f(x) \geq ax$ holds for $x \in [0, +\infty)$, find the range of values for $a$.

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