
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
For each positive integer  $k$  denote  $C(k)$  to be sum of its distinct prime divisors. For example  $C(1)=0,C(2)=2,C(45)=8$ . Find all positive integers  $n$  for which  $C(2^n+1)=C(n)$ .

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