
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 all  $n$  natural numbers such that for each of them there exist  $p , q$  primes such that these terms satisfy. $1.$   $p+2=q$  $2.$   $2^n+p$  and  $2^n+q$  are primes.

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