If $\tan x+\tan y=4$ and $\cot x+\cot y=5$, compute $\tan (x+y)$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $\tan x+\tan y=4$ and $\cot x+\cot y=5$, compute $\tan (x+y)$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
20
If $\tan x+\tan y=4$ and $\cot x+\cot y=5$, compute $\tan (x+y)$.
train