
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 $37$ terms; each term has the form $Q+n$ where $Q$ is the product $2 \times 3 \times 5 \times\ldots \times 53$ of all prime numbers less than or equal to $53$, and $n$ takes successively the values $4, 5, 6,\ldots, 40$. Let $M$ be the number of primes appearing in this sequence. Determine $M$.

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