
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 $f(x) = (ax+1)e^x - (a+1)x - 1$.  
(1) Find the equation of the tangent line to $y=f(x)$ at $(0, f(0))$.  
(2) If for $x > 0$, the inequality $f(x) > 0$ always holds, find the range of values for $a$.

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