
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 equation of curve $C$ is $mx^{2}+ny^{2}=1 (m > 0, n > 0)$, and the curve passes through points $A( \frac { \sqrt {2}}{4}, \frac { \sqrt {2}}{2})$ and $B( \frac { \sqrt {6}}{6}, \frac { \sqrt {3}}{3})$. $O$ is the coordinate origin.
(I) Find the equation of curve $C$;
(II) Let $M(x_{1},y_{1})$ and $N(x_{2},y_{2})$, and vectors $ \overrightarrow{p}( \sqrt {m}x_{1}, \sqrt {n}y_{1})$ and $ \overrightarrow{q}=( \sqrt {m}x_{2}, \sqrt {n}y_{2})$ with $ \overrightarrow{p} \cdot \overrightarrow{q}=0$. If line $MN$ passes through point $(0, \frac { \sqrt {3}}{2})$, find the slope of line $MN$.

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