
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 point P $(a, 0)$, the parametric equation of line $l$ is $$\begin{cases} x= \frac { \sqrt {3}}{2}t+a \\ y= \frac {1}{2}t \end{cases}$$ (where $t$ is the parameter). With the origin of the Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C$ is $\rho=2\cos\theta$.  
(Ⅰ) Find the general equation of line $l$ and the general equation of curve $C$;  
(Ⅱ) Given $a>1$, if line $l$ intersects curve $C$ at two points $A$ and $B$, and $|PA|\cdot|PB|=1$, find the value of the real number $a$.

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