
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 foci of the ellipse E are on the x-axis in the standard equation and it passes through the point $M(1, \frac{\sqrt{2}}{2})$, one of its foci coincides with the focus of the parabola $y^2=4x$. The upper vertex of ellipse E is A. The line passing through point N(0, 3) intersects the ellipse at points B and C. The slopes of lines AB and AC are denoted as $k_1$ and $k_2$, respectively.

(1) Find the standard equation of ellipse E;
(2) Calculate the value of $k_1 k_2$.

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