
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 a function $f(x)$ ($x \in \mathbb{R}$) that satisfies $f(1) = 1$, and the derivative of $f(x)$, $f'(x) < \frac{1}{2}$, then the solution set of the inequality $f(x) < \frac{x}{2} + \frac{1}{2}$ with respect to $x$ is \_\_\_\_\_\_.

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