
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
A 5-digit positive integer is defined as cute if its $n$ digits (where $n=5$) are an arrangement of the set $\{1, 2, 3, 4, 5\}$ and its first $k$ digits form an integer that is divisible by $k$, for $k = 1, 2, ..., 5$. Determine how many cute 5-digit integers exist.
A) 0
B) 1
C) 2
D) 3
E) 4

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