
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 $f(x)$ such that for any $x$, $y \in \mathbb{R}$, we have $f(x) + f(y) = f(x+y)$. When $x > 0$, $f(x) > 0$, and $f\left(-\frac{1}{4}\right) = -1$, then the solution set of the inequality $f(x^{2}-8) < 4$ is ______.

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