
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 functions $f(x) = (2x - 1)e^x$ and $g(x) = ax - a$ (where $a \in \mathbb{R}$).
1. If $y = g(x)$ is a tangent line of the curve $y = f(x)$, find the value of the real number $a$.
2. If $a < 1$, and the integer solution for the inequality $f(x) < g(x)$ is a single value $x_0$, find the range of values for the real number $a$.

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