
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 the curve $C$ are given by $\begin{cases} x=\sqrt{2}\cos\alpha \\ y=\sin\alpha \end{cases}$ where $\alpha$ is the parameter. Establish a polar coordinate system with $O$ as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of the line $l$ is $\theta=\frac{\pi}{4}$ ($\rho\in R$).

(1) Find the Cartesian coordinates of the intersection point(s) of the line $l$ and the curve $C$.
(2) Find the maximum distance from a point $P$ on the curve $C$ to the line $l$.

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