
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
Using the digits 1, 2, 3, and 4, form a four-digit number \(\overline{abcd}\) with the following conditions:
1. \(a, b, c,\) and \(d\) are all different.
2. \(b\) is greater than both \(a\) and \(d\), and \(c\) is greater than both \(a\) and \(d\). 

How many such four-digit numbers exist?

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