
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
You are given a sequence of $60$ terms; each term has the form $Q + n$ where $Q$ is the product $2 \times 3 \times 5 \times \ldots \times 59$ of all prime numbers less than or equal to $59$, and $n$ takes successively the values $1, 2, 3, \ldots, 60$. Determine the number of primes appearing in this sequence.

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