
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
Suppose the curve C has the polar coordinate equation $ρ\sin^2θ - 8\cos θ = 0$. Establish a rectangular coordinate system $xoy$ with the pole as the origin and the non-negative semi-axis of the polar axis as the $x$-axis. A line $l$, with an inclination angle of $α$, passes through point $P(2, 0)$.

(1) Write the rectangular coordinate equation of curve C and the parametric equation of line $l$.
(2) Suppose points $Q$ and $G$ have polar coordinates $\left(2, \dfrac{3π}{2}\right)$ and $\left(2, π\right)$, respectively. If line $l$ passes through point $Q$ and intersects curve $C$ at points $A$ and $B$, find the area of triangle $GAB$.

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