
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
An ellipse $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ has its left and right vertices coinciding with the left and right foci of a hyperbola $C′$: $x^{2}-y^{2}=2$. The eccentricities of the ellipse $C$ and hyperbola $C′$ are reciprocals of each other.
(I) Find the equation of the ellipse $C$;
(II) A line $l$ passing through point $Q(1,0)$ intersects the ellipse $C$ at points $A$ and $B$. Let $P(4,3)$, and denote the slopes of lines $PA$ and $PB$ as $k_{1}$ and $k_{2}$, respectively. Find the equation of line $l$ when $k_{1}⋅k_{2}$ is at its maximum.

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