
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 Cartesian coordinate system with origin $O$ and positive $x$-axis, a polar coordinate system is established. The polar equation of a semicircular curve $C$ is given by $p=2\cos\theta$, where $\theta \in [0, \frac{\pi}{2}]$. Find the parametric equation for curve $C$.

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