
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
If: (1) \( a, b, c, d \) are all elements of \( \{1,2,3,4\} \); (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, how many different four-digit numbers \( \overline{abcd} \) can be formed?

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