
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 Cartesian coordinate system, the parametric equations of the line $l$ are 
$$
\begin{cases}
x=1+t \\
y=t-3
\end{cases}
\quad (t \text{ is the parameter})
$$
In the polar coordinate system with the origin $O$ as the pole and the positive $x$-axis as the initial line, the polar equation of curve $C$ is 
$$
ρ= \dfrac {2\cos θ}{\sin^{2}\theta}
$$
(1) Find the Cartesian coordinate equation of curve $C$ and the general equation of line $l$;
(2) If line $l$ intersects curve $C$ at points $A$ and $B$, find the area of triangle $\triangle AOB$.

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