
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
If a three-digit positive integer "a<sub>1</sub>a<sub>2</sub>a<sub>3</sub>" satisfies $a_1 < a_2$, $a_3 < a_2$, then such a three-digit number is called a convex number (such as 120, 343, 275, etc.). How many convex numbers are there in total?

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