
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 positive integer $a_1a_2…a_n…a_{2n-2}a_{2n-1}$ is called a concave number if $a_1 > a_2 > … > a_n$ and $a_{2n-1} > a_{2n-2} > … > a_n$, where $a_i$ ($i=1,2,3,…$) $\in \{0,1,2,…,9\}$. Please answer how many three-digit concave numbers $a_1a_2a_3$ ($a_1 \neq a_3$) there are in total (answer in digits).

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