
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 that the center of an ellipse is at the origin, and it passes through the point $(1, \dfrac{3}{2})$ on the $x$-axis. The eccentricity of the ellipse is the reciprocal of the eccentricity of the hyperbola $x^{2}- \dfrac{y^{2}}{3}=1$.
(I) Find the equation of the ellipse;
(II) Given point $P( \dfrac{1}{5},0)$, if line $y=kx+m(k\neq 0)$ intersects the ellipse at two distinct points $M$ and $N$, and $|MP|=|NP|$, find the range of values for $k$.

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