
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
In the Cartesian coordinate system $xOy$, there is a curve $C$: $(x-1)^{2}+y^{2}=1$. A line $l$ passes through the point $P(m,0)$ and has an inclination angle of $\dfrac{\pi}{6}$. Establish a polar coordinate system with $O$ as the pole and the positive half-axis of $x$ as the polar axis.  
(Ⅰ) Write the polar equation of curve $C$ and the parametric equation of line $l$;  
(Ⅱ) If line $l$ intersects curve $C$ at points $A$ and $B$, and $|PA|\cdot|PB|=1$, find the value of the real number $m$.

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