
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, establish a polar coordinate system with the origin as the pole, the positive semi-axis of the $x$-axis as the polar axis, and the same unit of length. Given that the polar coordinate equation of line $l$ is $ρ \cos (θ + \dfrac{π }{3})=3$, and the polar coordinate equation of curve $C$ is $ρ =4a\cos θ (a > 0)$.

(1) Let $t$ be a parameter, if $y=-2\sqrt{3}+\dfrac{1}{2}t$, find the parametric equation of line $l$;

(2) Given that line $l$ intersects curve $C$ at points $P,Q$, set $M(0,-2\sqrt{3})$, and $|PQ{{|}^{2}}=|MP||MQ|$, find the value of real number $a$.

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