
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 $(xOy)$, the parametric equations of line $l$ are given by $\begin{cases} x=t+\sqrt{3}m \\ y=-\sqrt{3}t-2m \end{cases} (t \text{ is the parameter})$, and the polar equation of curve $C$ is $\rho(1-\cos 2\theta)=8\cos \theta$.

(1) Find the Cartesian equation of curve $C$;

(2) If line $l$ is tangent to curve $C$, find the area of the triangle formed by line $l$ and the coordinate axes.

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