
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
Given the parametric equations of line $l$ as $ \begin{cases} x=-\frac{3}{2}+t\cos\alpha \\ y=\frac{1}{2}+t\sin\alpha \end{cases} (t\text{ is the parameter})$, with $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis, establish a polar coordinate system. The polar equation of curve $C$ is given by $\rho=\rho\cos\theta+2, (\theta\in[0,2\pi))$.

1. Write the rectangular coordinates of the fixed point through which line $l$ passes and find the ordinary equation of curve $C$.
2. If $\alpha=\frac{\pi}{4}$, find the polar equation of line $l$ and the polar coordinates of the intersection point(s) of line $l$ and curve $C$.

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