
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 equation of curve $C$ as $ \begin{cases} x=\cos \alpha -1 \\ y=\sin \alpha +1 \\ \end{cases} (\alpha \text{ is the parameter})$, where point $P$ is a moving point on curve $C$, and $O$ is the origin of the coordinate system. Find the minimum value of $|PO|$.

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