
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
What is the total number of three-digit convex numbers, such numbers are defined by having their hundred's digit less than their ten's digit and their ten's digit greater than their one's digit (e.g., 120, 352)?

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