
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
A. In the rectangular coordinate system $(xOy)$, the equation of curve $(C_{1})$ is $y=k|x|+2$. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equation of curve $(C_{2})$ is $(ρ^{2}+2ρ\cos⁡θ−3=0)$.
(1) Find the rectangular coordinate equation of $(C_{2})$;
(2) If $(C_{1})$ and $(C_{2})$ have exactly three common points, find the equation of $(C_{1})$.

B. It is known that $f(x)=|x+1|−|ax−1|$.
(1) When $a=1$, find the solution set of the inequality $f(x) > 1$;
(2) If the inequality $f(x) > x$ holds when $x∈(0,1)$, find the range of values of $a$.

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