
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]


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Given a function $f(x)$ defined on $\mathbb{R}$ is an increasing function, and when $x_1 + x_2 = 1$, the inequality $f(x_1) + f(0) > f(x_2) + f(1)$ always holds, determine the range of values for the real number $x_1$.

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