
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 parametric equation of the line as $\begin{cases} & x=t+3 \\\\ & y=3-t \end{cases}$, and the parametric equation of circle $C$ as $\begin{cases} & x=2\cos \theta \\\\ & y=2\sin \theta +2 \end{cases}$, find the distance from the circle's center to the line.

2. If $f(x)={{({{a}^{2}}-1)}^{x}}$ is a monotonically decreasing function for all $x\in R$, find the range of values for $a$.

3. Given the function $f\left( x \right)={{e}^{x}}-{\dfrac{1}{2}{{x}^{2}}-ax\left( a\in R \right)}$, if the equation of the tangent line to the graph of the function at $x=0$ is $y=2x+b$, find the value of $a+b$.

4. Determine the sequence numbers of the true statements among the following four propositions:

   ① The converse of the statement "If $x+y=0$, then $x$ and $y$ are opposite numbers"

   ② The negation of the statement "If ${x}^{2}+x-6\geqslant 0 $, then $x > 2$"

   ③ In $\triangle ABC$, "$A > 30^{\circ}$" is a necessary but not sufficient condition for "$\sin A > \dfrac{1}{2} $"

   ④ The necessary and sufficient condition for the function $f(x)=\tan (x+φ) $ to be an odd function is "$φ=kπ(k∈Z) $"

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