
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 represented by the parametric equations \(\begin{cases} x = 2 \cos \alpha \\ y = \sin \alpha \end{cases} (\alpha \text{ is the parameter})\). Utilizing the origin \(O\) as the pole and the non-negative half of the \(x\)-axis as the polar axis, a polar coordinate system is established.  
\((1)\) Find the polar equation for curve \(C\);  
\((2)\) Let \(A\) and \(B\) be any two points on curve \(C\), and suppose \(OA \perp OB\), determine the range of values for \(|AB|\).

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