
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 $xOy$, the left and right foci of the ellipse $C_1$: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1 \ (a>b>0)$$ are $F_1$ and $F_2$, respectively, where $F_2$ is also the focus of the parabola $C_2$: $y^2=4x$. Point $M$ is the intersection of $C_1$ and $C_2$ in the first quadrant, and $|MF_2|= \frac {5}{3}$.  
(1) Find the equation of the ellipse;  
(2) If a line $l$ passing through point $D(4,0)$ intersects $C_1$ at two distinct points $A$ and $B$, and $A$ is between $D$ and $B$, find the range of the ratio of the areas of $\triangle AOD$ and $\triangle BOD$.

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