
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 three-digit number is called a "concave number" if the digit in the tens place is smaller than both the digit in the hundreds place and the digit in the units place. For example, 504 and 746 are concave numbers. How many three-digit concave numbers are there if all the digits are distinct?

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