
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 curve $C$ are $\left\{\begin{array}{l}x=2\cos\alpha\\ y=\sin\alpha\end{array}\right.$ ($\alpha$ is the parameter). The parametric equation of line $l$ is established with $O$ as the pole and the non-negative x-axis as the polar axis. The polar equation of line $l$ is $ρ\sin(θ+\frac{π}{4})=\frac{\sqrt{2}}{2}$. <br/>$(1)$ Find the general equations of curve $C$ and line $l$; <br/>$(2)$ Let the polar coordinates of point $A$ be $(2,\frac{π}{6})$. Curve $C$ and line $l$ intersect at $P$ and $Q$. Find the area of $\triangle APQ$.

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