
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 the smallest possible number of divisors a positive integer  $n$  may have, which satisfies the following conditions:
1.  $24 \mid n+1$ ;
2. The sum of the squares of all divisors of  $n$  is divisible by  $48$  ( $1$  and  $n$  are included).

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