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

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