
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
A hyperbola in the coordinate plane passing through the points  $(2,5)$ ,  $(7,3)$ ,  $(1,1)$ , and  $(10,10)$  has an asymptote of slope  $\frac{20}{17}$ . The slope of its other asymptote can be expressed in the form  $-\frac{m}{n}$ , where  $m$  and  $n$  are relatively prime positive integers. Compute  $100m+n$ .

*Proposed by Michael Ren*

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