
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 the curve $C$ are given by $\begin{cases} x=\cos \alpha \\ y=1+\sin ^{2}\alpha \end{cases} (\alpha \text{ is the parameter})$, and the polar coordinate system is established with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of the line $l$ is $\theta= \dfrac {\pi}{4}$. Find the rectangular coordinates of the intersection point of the line $l$ and the curve $C$.

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