
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 the line $l: \begin{cases} x=m+t\cos \alpha \\ y=t\sin \alpha \end{cases} (t\text{ is a parameter})$, which passes through the left focus $F$ of the ellipse $C: \begin{cases} x=2\cos \phi \\ y=\sqrt {3}\sin \phi \end{cases} (\phi\text{ is a parameter})$.

(1) Find the value of $m$;

(2) Suppose the line $l$ intersects the elliptic curve $C$ at points $A$ and $B$, find the maximum and minimum values of $|FA|\cdot|FB|$.

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