
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
The function $f(x)$ ($x \in \mathbb{R}$) satisfies $f(1)=1$ and $f'(x) < \frac{1}{2}$. The solution set of the inequality $f(x^{2}) < \frac{x^{2}}{2} + \frac{1}{2}$ is \_\_\_\_\_\_.

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