
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
(The choice of coordinate system and parametric equations) The number of intersection points between the curve $\begin{cases} x=\cos\alpha \\ y=1+\sin\alpha \end{cases}$ (where $\alpha$ is the parameter) and the curve $\rho^2-2\rho\cos\theta=0$ is ______________.

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