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

(I) Determine the value of $m$.

(II) If the line $l$ intersects the 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}
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