
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) The negation of the proposition "$\forall x \in \mathbb{R}, \sin x \leqslant 1$" is.

(2) In $\triangle ABC$, if $\frac{\cos A}{\cos B} = \frac{\sin B}{\sin A}$, then the shape of $\triangle ABC$ is.

(3) Given the parametric equation of curve $C_{1}$ is $\begin{cases} x=\sqrt{t} \\ y=\frac{\sqrt{3t}}{3} \end{cases}$ ($t$ is the parameter). Establishing a polar coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_{2}$ is $\rho=2$. The rectangular coordinates of the intersection point of $C_{1}$ and $C_{2}$ are.

(4) For any $a \in [-1,1]$, the function $f(x) = x^{2} + (a-4)x + 4 - 2a$ is always greater than zero, then the range of $x$ is.

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