
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
Let $f(x)$ be a decreasing function defined on $\mathbb{R}$, and it satisfies $f(n^2 - 10n - 15) \geq f(12 - m^2 + 24m)$. Find the range of values for $m^2 + n^2$.

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