
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 that the function $f(x)$ defined on $\mathbb{R}$ satisfies $f(x) + f(-x) = 0$, and $\frac{f(x\_1) - f(x\_2)}{x\_1 - x\_2} < 0$ on $(-∞, 0)$, with $f(5) = 0$, determine the range of $x$ for which $f(x) < 0$.

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