
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 that in the rectangular coordinate system $(xOy)$, the parametric equations of the curve $C$ are $ \begin{cases} x=1+4\cos θ \\ y=2+4\sin θ \end{cases}(θ $ is the parameter$), and the line $l$ passes through the fixed point $P(2,1)$ with an angle of inclination of $ \dfrac {π}{6}$.
(1) Write out the parametric equations of the line $l$ and the general equation of the curve $C$.
(2) Suppose the line $l$ intersects the curve $C$ at points $A$ and $B$. Determine the value of $|PA|⋅|PB|$.

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