
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 $(xOy)$, a line $l$ passes through the point $(1,0)$ with an angle of inclination $\alpha$. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar equation of the curve $C$ is $\rho=\frac{8\cos\theta}{1-\cos^{2}\theta}$.

(1) Write the parametric equation of the line $l$ and the rectangular equation of the curve $C$.
(2) If $\alpha=\frac{\pi}{4}$, and the line $l$ intersects the curve $C$ at points $A$ and $B$, find the area of $\triangle AOB$.

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