<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Let  $\underline{xyz}$  represent the three-digit number with hundreds digit  $x$ , tens digit  $y$ , and units digit  $z$ , and similarly let  $\underline{yz}$  represent the two-digit number with tens digit  $y$  and units digit  $z$ .  How many three-digit numbers  $\underline{abc}$ , none of whose digits are 0, are there such that  $\underline{ab}>\underline{bc}>\underline{ca}$ ? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
120
Let  $\underline{xyz}$  represent the three-digit number with hundreds digit  $x$ , tens digit  $y$ , and units digit  $z$ , and similarly let  $\underline{yz}$  represent the two-digit number with tens digit  $y$  and units digit  $z$ .  How many three-digit numbers  $\underline{abc}$ , none of whose digits are 0, are there such that  $\underline{ab}>\underline{bc}>\underline{ca}$ ?
test