
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 \( xoy \), the curve \( C \) is given by the parametric equations 
$$ \begin{cases} x = \cos \alpha + 1 \\ y = \sin \alpha \end{cases} (\alpha \) is the parameter). 
Now, with \( O \) as the pole and the positive x-axis as the polar axis, establish a polar coordinate system and derive the polar equation of curve \( C \).

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