
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
Let  $(a_{n})_{n\geq 1}$  be a sequence defined by  $a_{n}=2^{n}+49$ . Find all values of  $n$  such that  $a_{n}=pg, a_{n+1}=rs$ , where  $p,q,r,s$  are prime numbers with  $p<q, r<s$  and  $q-p=s-r$ .

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