
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 positive integer  $n > 1$  is juicy if its divisors  $d_1 < d_2 < \dots < d_k$  satisfy  $d_i - d_{i-1} \mid n$  for all  $2 \leq i \leq k$ . Find all squarefree juicy integers.

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