
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
Determine all pairs of prime numbers  $p$  and  $q$  greater than  $1$  and less than  $100$ , such that the following five numbers:   $$ p+6,p+10,q+4,q+10,p+q+1, $$   are all prime numbers.

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