
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 $50$ terms; each term is given by $Q + m$, 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 $m$ takes successively the values $2, 3, 4, \ldots, 51$. Calculate the number of terms in this sequence that are divisible by $53$.

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