
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 $C_1$: $\frac{{x}^{2}}{{a}^{2}}$ + $\frac{{y}^{2}}{{b}^{2}}$ = 1 (a > b > 0) with its right focus F coinciding with the focus of the parabola $C_2$, and the center of $C_1$ coinciding with the vertex of $C_2$. A line passing through F and perpendicular to the x-axis intersects $C_1$ at points A and B, and intersects $C_2$ at points C and D, where |CD| = $\frac{4}{3}$|AB|. <br /> (1) Find the eccentricity of $C_1$; <br /> (2) If the sum of the distances from the four vertices of $C_1$ to the directrix of $C_2$ is 12, find the standard equations of $C_1$ and $C_2$.

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