
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
In the Cartesian coordinate system, there exists an ellipse C<sub>1</sub>: $\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$ ($a > b > 0$) with an eccentricity $e= \frac {\sqrt {3}}{2}$, and the length of the minor axis of the ellipse C<sub>1</sub> is 2.  
(1) Determine the equation of the ellipse C<sub>1</sub>.  
(2) Let A(0, $\frac{1}{16}$) and let N be a moving point on the parabola C<sub>2</sub>: $y=x^{2}$. A tangent to the parabola C<sub>2</sub> at point N intersects the ellipse C<sub>1</sub> at points B and C. Find the maximum area of triangle ABC.

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