
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) = e^(x+1) - e^x + x^2 + 2m(x-1) (m > 0) defined on R, the inequality f(x1) ≥ f(x2) always holds true when x1 + x2 = 1. Determine the range of values for the real number x1.

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