
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
Among three-digit numbers, if the digit in the tens place is smaller than both the digits in the units and hundreds places, then this three-digit number is called a "concave number," such as 402, 745, etc. How many three-digit concave numbers are there with no repeated digits in each place?

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