
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
Find how many cute 4-digit integers exist where a cute integer is defined such that its digits are an arrangement of the set $\{1, 2, 3, 4\}$ and the integer formed by the first k digits is divisible by k for each \(k = 1, 2, 3, 4\).
A) 0
B) 1
C) 2
D) 3
E) 4

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