
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 integer  $n$  is called *apocalyptic* if the addition of  $6$  different positive divisors of  $n$  gives  $3528$ . For example,  $2012$  is apocalyptic, because it has six divisors,  $1$ ,  $2$ ,  $4$ ,  $503$ ,  $1006$  and  $2012$ , that add up to  $3528$ .

Find the smallest positive apocalyptic number.

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