
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 that: (1) $a$, $b$, $c$, $d$ all belong to $\{1, 2, 3, 4\}$;  
(2) $a \neq b$, $b \neq c$, $c \neq d$, $d \neq a$;  
(3) $a$ is the smallest value among $a$, $b$, $c$, $d$,  
then, the number of different four-digit numbers that can be formed is $\boxed{\text{\_\_\_\_\_\_\_\_\_}}$.

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