
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 trapezoid  $ABCD$  lies on the  $xy$ -plane. The slopes of lines  $BC$  and  $AD$  are both  $\frac 13$ , and the slope of line  $AB$  is  $-\frac 23$ . Given that  $AB=CD$  and  $BC< AD$ , the absolute value of the slope of line  $CD$  can be expressed as  $\frac mn$ , where  $m,n$  are two relatively prime positive integers. Find  $100m+n$ .

*Proposed by Yannick Yao*

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