
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_1 a_2 a_3 a_4 a_5} \\), where \\(a_i \in \{0,1,2,3,4,5\}\\) for \\(i=1,2,3,4,5\\), is called a "concave number" if and only if \\(a_1 > a_2 > a_3\\) and \\(a_3 < a_4 < a_5\\) (e.g., 32014, 53134). Find the number of such concave five-digit natural numbers.

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