
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 $y=f(x)$ is an increasing function defined on $\mathbb{R}$, and the graph of $y=f(x)$ is symmetric about the point $(0,0)$. If the real numbers $x, y$ satisfy the inequality $f(x^2-6x)+f(y^2-8y+24)<0$, then the range of values for $x^2+y^2$ is.

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