
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 ellipse $C: \frac{x^{2}}{3m}+ \frac{y^{2}}{m}=1$, and the line $l$: $x+y-2=0$. The line intersects the ellipse at two points $P$ and $Q$, and intersects the $x$-axis at point $B$. Points $P$ and $Q$ do not coincide with point $B$.
(I) Find the eccentricity of the ellipse $C$;
(II) When the area of $\triangle OPQ$ is 2, find the equation of the ellipse $C$;
(III) Draw a line perpendicular to line $l$ passing through the origin $O$, with the foot of the perpendicular being $N$. If $|PN|=λ|BQ|$, find the value of $λ$.

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