
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 termed adorable if its digits are a rearrangement of $\{1, 2, 3, 4, 5\}$ and the integer formed by its first $k$ digits is divisible by $k$ for each $k = 1, 2, 3, 4, 5$. Additionally, the sum of its digits must be divisible by 5. Find the number of adorable 5-digit integers.
A) 0
B) 1
C) 2
D) 3
E) 4

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