
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 rectangular coordinate system $xOy$, establish a polar coordinate system with the origin as the pole and the positive semi-axis of $x$ as the polar axis. Given that the polar coordinate equation of the curve $C$ is $ρ=4$, and the parametric equation of the line $l$ is $$\begin{cases} x=a+t\cos{α} \\ y=b+t\sin{α} \end{cases}$$ (where $t$ is the parameter).
(1) If $a=8$, $b=0$, and $α= \frac {π}{3}$, determine the positional relationship between line $l$ and curve $C$;
(2) If point $P(a,b)$ is inside curve $C$, and line $l$ intersects curve $C$ at points $A$ and $B$, such that $|PA|$, $|OP|$, and $|PB|$ form a geometric sequence, find the trajectory equation of the moving point $P(a,b)$.

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