
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 $f(x)$ is an even function defined on $\mathbb{R}$ with its derivative $f′(x)$, when $x∈(-∞,0]$, $f(x)$ has a unique zero point $-3$, and $xf′(x) < f(-x)$ always holds. Determine the range of real number $x$ that satisfies the inequality $\frac {f(x)}{x}\leqslant 0$. (Express the result in set or interval form)

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