
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 a circle $C$ as follows:
$$
\begin{cases}
x = \cos\alpha \\
y = 1 + \sin\alpha
\end{cases}
$$
where $\alpha$ is the parameter. Establish a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis. The polar equation of line $l$ is $p\sin\theta = 1$. Find the Cartesian coordinates of the intersection points between line $l$ and circle $C$.

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