
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 a line $l$: $\begin{cases} x=2+t\cos \alpha \\ y=t\sin \alpha \end{cases}$ (where $t$ is a parameter), and an ellipse $C$: $\begin{cases} x=3\cos \phi \\ y= \sqrt {5}\sin \phi \end{cases}$ (where $\phi$ is a parameter), $F$ is the right focus of the ellipse $C$.  
$(1)$ When $\alpha= \frac {\pi}{4}$, with the origin as the pole and the positive half-axis of $x$ as the polar axis, establish a polar coordinate system and find the polar equations of line $l$ and curve $C$;  
$(2)$ Suppose line $l$ intersects ellipse $C$ at points $A$ and $B$, find the maximum and minimum values of $|FA|\cdot|FB|$.

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