
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 $f(x) = a + (bx-1)e^x$ (where $a, b \in \mathbb{R}$):  
(1) If the tangent line to the curve $y=f(x)$ at the point $(0, f(0))$ is $y=x,$ determine the values of $a$ and $b$.  
(2) If $a<1$ and $b=2$, find the range of $a$ for which the inequality $f(x) < ax$ has exactly one integer solution.

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