
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 an "umbrella number" if the digit in the tens place is larger than the digits in both the ones and hundreds places. If one selects three distinct digits from the set {1, 2, 3, 4, 5, 6} to form a three-digit number without repeating any digits, the number of "umbrella numbers" that can be formed is ______.

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