
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  $a$  and  $b$  be positive integers not divisible by  $5$ . A sequence of integers is constructed as follows: the first term is  $5$ , and every consequent term is obtained by multiplying its precedent by  $a$  and adding  $b$ . (For example, if  $a = 2$  and  $b = 4$ , the first three terms are  $5,14,32$ .) What is the maximum possible number  of primes that can occur before encoutering the first composite term?

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