
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 three-digit numbers, if the digit in the tens place is smaller than the digits in both the hundreds and ones places, the number is called a "concave number," such as 304, 968, etc. How many distinct three-digit concave numbers are there without any repeated digits?

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