
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
(I) Given the function $f(x)=45|2x+2|-45|x-2|$,
(1) Find the solution set of the inequality $f(x)>2$;
(2) For $x\in R$, if $f(x)\geq t^{2}-\frac{7}{2}t$ always holds, find the range of values for the real number $t$.
(II) In the rectangular coordinate system $xOy$, the parametric equations of the curve $C_{1}$ are given by $\begin{cases} x=1+2\cos\theta\\ y=2\sin\theta \end{cases}$ ($\theta$ is the parameter). Establish a polar coordinate system with $O$ as the pole and the non-negative semi-axis of the $x$-axis as the polar axis.
(1) Find the general equation of the curve $C_{1}$;
(2) Find the length of the line segment $PQ$, where the line $l$ with the polar equation $2\rho\sin(\theta+\frac{\pi}{3})=3\sqrt{3}$ intersects with $C_{1}$ at points $P$ and $Q$.

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