
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
An $n$-digit positive integer is described as majestic if its $n$ digits form a permutation of the numbers $\{1, 2, ..., n\}$ and the number formed from its first $k$ digits is divisible by $k$ for every $k = 1, 2, ..., n$. Determine how many majestic $4$-digit integers exist.
A) 0
B) 1
C) 2
D) 3
E) 4

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