
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 polar coordinate system, the polar coordinate equation of the line $l$ is $θ= \dfrac {π}{3}(ρ∈R)$. Establish a Cartesian coordinate system with the pole as the origin and the positive half of the polar axis as the $x$-axis. The parametric equations of the curve $C$ are $ \begin{cases} x=2\cos α \\ y=1+\cos 2α \end{cases}(α \text{ is the parameter})$. Find the Cartesian coordinates of the intersection point $P$ of the line $l$ and the curve $C$.

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