
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 an ellipse $E$ described by the equation $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1$ ($a > b > 0$) that passes through the point $(0,1)$ and has an eccentricity $e= \dfrac { \sqrt {2}}{2}$,  
(I) find the equation of the ellipse $E$;  
(II) suppose a moving line $l$ intersects with two fixed lines $l_1$: $x-y=0$ and $l_2$: $x+y=0$ at points $P$, $Q$ respectively. If $l$ always intersects ellipse $E$ at only one point, investigate whether the area of $\triangle OPQ$ has a minimum value. If a minimum value exists, find it; if it does not exist, explain why.

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