
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 curve $C$ is $\begin{cases}x=3\sec \theta \\ y=4\tan \theta\end{cases} (\theta$ is the parameter$)$, then the eccentricity of curve $C$ is _______.

(2) Given the polar equations of curves $C^{1}C^{2}$ are $\rho\cos \theta=3, \rho=4\cos \theta, (\rho\geqslant 0,0\leqslant \theta < \frac{\pi}{2})$, then the polar coordinates of the intersection point of curve $C1C2$ are _______.

(3) The equation of the axis of symmetry for the function $f(x)=\cos 2x-2 \sqrt{3}\sin x\cos x$ is ______________.

(4) Suppose the parametric equation of line $l_{1}$ is $\begin{cases}x=1+t \\ y=1+3t\end{cases} (t$ is the parameter$)$, and the equation of line $l_{2}$ is $y=3x+4$, then the distance between $l_{1}$ and $l_{2}$ is _______.

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