
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 curve $C:\dfrac{4x^{2}}{9}+\dfrac{y^{2}}{16}=1$ and the line $l:\begin{cases}x=3+t \\ y=5-2t\end{cases} (t$ is a parameter$)$

(a) Write the parametric equation of the curve $C$ and the general equation of the line $l$.
(b) Let $P$ be any point on the curve $C$ and $d$ be the distance from $P$ to the line $l$. Find the maximum and minimum values of $d$.

(2) Given the functions $f(x)=2\left| x+1 \right|-a,g(x)=\left| x \right|$
(a) If $a=0$, solve the inequality $f(x)\geqslant g(x)$;
(b) If there exists $x\in R$, such that the inequality $f(x)\geqslant 2g(x)$ holds, find the range of values for the real number $a$.

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