
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
In an ellipse, there is a conclusion that the midpoint of the chord with a slope of 1 on the ellipse $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1(a > b > 0)$ is located on the line $\frac{x}{{{a}^{2}}}+\frac{y}{{{b}^{2}}}=0$. By analogy with the above conclusion, the midpoint of the chord with a slope of 1 on the hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1(a > 0,b > 0)$ is located on the line \_\_\_\_\_\_\_\_.

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