
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 $(xOy)$, the parametric equations of line $l$ are given by $\begin{cases} & x=1+t, \\ & y=t-3 \end{cases}$ $(t$ is a parameter$)$, and the polar coordinate equation of curve $C$ with origin $O$ as the pole and positive $x$-axis as the polar axis is $\rho = \frac{2\cos \theta}{\sin^2\theta}$. If line $l$ intersects curve $C$ at points $A$ and $B$, find the area of $\triangle AOB$.

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