
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
Consider a sequence of $64$ terms, each with the form $Q+m$ where $Q$ is the product $2 \times 3 \times 5 \times \ldots \times 67$ of all prime numbers less than or equal to $67$, and $m$ successively takes the values $2, 3, 4, \ldots, 65$. Let $M$ be the number of primes appearing in this sequence. What is the value of $M$?

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