
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 $(a,b∈R)$,
(1) If the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$ is $y=x$, find the values of $a$ and $b$;
(2) If $a < 1$, $b=2$, and the inequality $f(x) < ax$ has exactly one integer solution with respect to $x$, find the range of $a$.

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