
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 domain of the function $f(x)$ is $R$, the graph of $f(x-1)$ is symmetric about the point $(1,0)$, $f(3)=0$, and for any $x_{1}$, $x_{2}\in (-\infty,0)$, $x_{1}\neq x_{2}$, it satisfies $\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}＜0$. Then solve the inequality $\left(x-1\right)f(x+1)\geqslant 0$.

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