
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 with the equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ ($a>b>0$) and having a focal length of 2 that passes through the point $(1, \frac{3}{2})$. Let the endpoints of the major axis be A and B, and let a line $y=\frac{3}{2}x+m$ intersect the ellipse at points C and D.
1. Find the standard equation of the ellipse.
2. Let the slopes of lines AD and BC be $k_1$ and $k_2$ respectively, and suppose the ratio of $k_1:k_2$ is 2:1. Determine the value of $m$.

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