
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 $m$, $n$, $s$, $t \in R^{+}$, $m+n=2$, $\frac{m}{s} + \frac{n}{t}=9$, where $m$, $n$ are constants, when $s+t$ takes the minimum value $\frac{4}{9}$, the corresponding point $(m, n)$ is the midpoint of a chord of the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{2} = 1$. The equation of the line on which this chord lies is ___.

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