
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
Given the parametric equations of curve $C_1$ are $$\begin{cases} x=4t \\ y=3t-1\end{cases}$$ (where $t$ is the parameter), when $t=0$, the corresponding point on curve $C_1$ is $P$. Taking the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_2$ is $\rho= \frac {8\cos\theta}{1-\cos2\theta}$.  
(I) Find the general equation of curve $C_1$ and the Cartesian coordinate equation of curve $C_2$;  
(II) Suppose the common points of curve $C_1$ and $C_2$ are $A$ and $B$, find the value of $|PA|\cdot|PB|$.

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