
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
For an integer  $n$  let  $M (n) = \{n, n + 1, n + 2, n + 3, n + 4\}$ . Furthermore, be  $S (n)$  sum of squares and  $P (n)$  the product of the squares of the elements of  $M (n)$ . For which integers  $n$  is  $S (n)$  a divisor of  $P (n)$  ?

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