
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 $xOy$, let the curve $C: x^{2}+y^{2}-2x=0$. There is a line $l$ passing through the point $P(m, 0)$ with an inclination angle of $ \dfrac {π}{6}$. Establish a polar coordinate system with $O$ as the pole and the positive $x$-axis as the polar axis.

(Ⅰ) Write the polar coordinate equation of the curve $C$ and the parametric equation of the line $l$.

(Ⅱ) If line $l$ intersects curve $C$ at points $A$ and $B$, and the product of the lengths $|PA|\cdot|PB|=1$, find the value of the real number $m$.

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