
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 parametric equation of line $l$ is
$$
\begin{cases}
x = -1 + \frac {\sqrt {2}}{2}t \\
y = 1 + \frac {\sqrt {2}}{2}t
\end{cases}
(t \text{ is the parameter}),
$$
and the equation of circle $C$ is $(x-2)^{2} + (y-1)^{2} = 5$. Establish a polar coordinate system with the origin $O$ as the pole and the positive $x$-axis as the polar axis.

(Ⅰ) Find the polar equations of line $l$ and circle $C$.

(Ⅱ) If line $l$ intersects circle $C$ at points $A$ and $B$, find the value of $\cos ∠AOB$.

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