
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 a 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 this conclusion, the midpoint of a chord with a slope of 1 on the hyperbola \\(\frac{{{x}^{2}}}{{{a}^{2}}}-\\frac{{{y}^{2}}}{{{b}^{2}}}=1(a,b > 0)\\) is located on the line \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

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