
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 number \(abcde\) satisfies:
\[ a < b, \, b > c > d, \, d < e, \, \text{and} \, a > d, \, b > e. \]

For example, 34 201, 49 412. If the digit order's pattern follows a variation similar to the monotonicity of a sine function over one period, then the five-digit number is said to follow the "sine rule." Find the total number of five-digit numbers that follow the sine rule.

Note: Please disregard any references or examples provided within the original problem if they are not part of the actual problem statement.

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