
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 five-digit natural number $\overline{a_1a_2a_3a_4a_5}$ is considered a "concave number" if and only if $a_1 > a_2 > a_3$ and $a_3 < a_4 < a_5$, with each $a_i \in \{0,1,2,3,4,5\}$ for $i=1,2,3,4,5$. Calculate the number of possible "concave numbers".

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