
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 $(m,n)$ corresponding to $m$, $n$ is the midpoint of a chord of the hyperbola $\frac{x^{2}}{4} - \frac{y^{2}}{2} = 1$. Then, the equation of the line containing this chord is \_\_\_\_\_\_.

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