
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 a regular triangle with side length $8\sqrt{3}$, one vertex is at the origin, and the other two vertices lie on the parabola $C: x^2 = 2py$ ($p>0$).

(1) Determine the equation of parabola $C$.

(2) Given a circle passing through a fixed point $D(0, 2)$, with the center $M$ moving along the parabola $C$, and the circle intersects with the x-axis at points $A$ and $B$. Let $|DA| = l_1$ and $|DB| = l_2$, find the maximum value of $\frac{l_1}{l_2} + \frac{l_2}{l_1}$.

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