
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
(1) Given the set $A={x|1 < x < 4}$, and set $B ={x|x^{2}-2x-3\leqslant 0}$, find $A∩(C\_RB)=$.

(2) In the polar coordinate system, the point symmetric to point $M(1,0)$ about the pole is (Note: ${0}\leqslant {\theta} < \frac{{\pi} }{2}$, $ρ > 0$).

(3) If $x,y\in R$, and $\frac{x}{1-i}-\frac{y}{1-2i}=\frac{5}{1-3i}$, find $x=$

(4) Given the function $f\left(x\right)={x}^{3}- \frac{1}{2}\sin x+3x $, for any $x∈R $, $f\left(-{x}^{2}+3x\right)+f\left(x-2k\right)\leqslant 0 $ always holds true. Find the range of values for $k$.

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