
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 rectangular coordinate system xOy, the point ($\frac{1}{2}$, $\sqrt{3}$) is on the curve C defined by the parametric equations {$x = k\cos\phi, y = k\sin\phi$} where $\phi$ is the parameter. The corresponding parameter for this point is $\phi = \frac{\pi}{3}$. Using the origin O as the pole and the positive semi-axis of x as the polar axis, a polar coordinate system is established. It is known that the polar coordinates of point P are (2, $\frac{\pi}{6}$).

1. Directly write the rectangular coordinates of point P and the polar equation of curve C.
2. Let A and B be two moving points on curve C such that OA is perpendicular to OB. Find the minimum value of $|OA|^2 + |OB|^2$.

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