
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:
(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 \(a, b, c, d\).
How many different four-digit numbers \(\overline{abcd}\) can be formed?

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