
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
Given the numbers 1, 2, 3, 4, 7, and 9.  
(1) How many five-digit numbers without repeated digits can be formed?  
(2) How many of these numbers are even?  
(3) How many of these numbers are multiples of 3?

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