
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 $f(x) = e^{ax} - x$.  
$(1)$ When $a=1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$.  
$(2)$ Find the intervals where $f(x)$ is monotonic.  
$(3)$ If there exist $x_{1}$ and $x_{2} \in [-1,1]$ such that $f(x_{1}) \cdot f(x_{2}) \geq 9$, find the range of values for $a$.

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