
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) Convert the polar coordinates $(2,\frac{\pi}{6})$ into Cartesian coordinates.

(2) Points $M$ and $N$ are on the curves $\rho\sin \theta=2$ and $\rho=2\cos \theta$, respectively. Find the minimum value of $|MN|$.

(3) Given the functions $f(x)=|x-a|+a$ and $g(x)=4-x^{2}$, if there exists $x\in\mathbb{R}$ such that $g(x)\geqslant f(x)$, find the range of values for $a$.

(4) Given $p: |1-\frac{x-1}{3}|\leqslant 2$ and $q: x^{2}-2x+1-m^{2}\leqslant 0$ ($m > 0$), and knowing that the negation of $p$ is a necessary but not sufficient condition for the negation of $q$, find the range of values for $m$.

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