
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 number in the form of $45132$ is called a "five-digit wave number," where the digit in the tens place and the digit in the thousands place are both larger than their respective adjacent digits. Determine the number of unique "five-digit wave numbers" that can be formed using the digits $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$.

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