
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
There are 10 digits from 0 to 9. How many distinct numbers can be formed that are:  
(1) five-digit numbers;  
(2) five-digit numbers greater than or equal to 30000;  
(3) among the five-digit numbers with distinct digits, what is the rank of 50124 in descending order?

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