
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 some positive integer  $n$ , consider the usual prime factorization \[n =
	\displaystyle \prod_{i=1}^{k} p_{i}^{e_{i}}=p_1^{e_1}p_2^{e_2}\ldots p_k^{e_k},\] where  $k$  is the number of primes factors of  $n$  and  $p_{i}$  are the prime factors of  $n$ . Define  $Q(n), R(n)$  by
	\[
		Q(n) = \prod_{i=1}^{k} p_{i}^{p_{i}} \text{ and } R(n) =
		\prod_{i=1}^{k} e_{i}^{e_{i}}.
	\] For how many  $1 \leq n \leq 70$  does  $R(n)$  divide  $Q(n)$ ?

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