
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) = x(e^x + 1) - a(e^x - 1),

1. Find the value of the real number a if the slope of the tangent line to the curve y = f(x) at the point (1, f(1)) is 1.
2. Find the range of values for the real number a such that f(x) > 0 is always true when x ∈ (0, +∞).

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