
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 $\overline{abcde}$ satisfies $a < b$, $b > c > d$, $d < e$, and $a > d$, $b > e$ (e.g., $37201$, $45412$). Such a number is said to follow the "sine law." Determine the number of five-digit numbers that follow the "sine law."

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