
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 that the parametric equation of curve C is $$\begin{cases} x=-1+ \sqrt {2}\cos\phi \\ y=1+ \sqrt {2}\sin\phi\end{cases}$$ (where $\phi$ is the parameter), establish a polar coordinate system with the origin O of the rectangular coordinate system as the pole and the positive half of the x-axis as the polar axis.

(I) Find the polar equation of curve C.
(II) Let lines $l_1$: $\theta= \frac {\pi}{3}$, $l_2$: $\theta= \frac {5\pi}{6}$, $\rho \in \mathbb{R}$. If $l_1$ and $l_2$ intersect with curve C at two points A and B, which are distinct from the origin O, find the area of triangle AOB.

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