
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 polar coordinate system, the polar coordinate equation of circle $C$ is $ρ^{2}-8ρ\sin (θ- \dfrac {π}{3})+13=0$. Given points $A(1, \dfrac {3π}{2})$ and $B(3, \dfrac {3π}{2})$, where $P$ is a point on circle $C$, find the minimum value of the area of $\triangle PAB$.

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