
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 $l: \begin{cases} x=t\cos α+m \\ y=t\sin α\end{cases} (t\text{ is a parameter})$ always passes through the ellipse $C: \begin{cases} x=5\cos φ \\ y=3\sin φ\end{cases} (φ\text{ is a parameter})$ at the right focus $F$.
(1) Find the value of $m$;
(2) Suppose the line $l$ intersects the ellipse $C$ at points $A$ and $B$, find the maximum and minimum values of $|FA|⋅|FB|$.

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