
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
Define the function $f_1$ on the positive integers by setting $f_1(1)=1$. For a positive integer $n > 1$ with prime factorization $n = p_1^{e_1} p_2^{e_2} \cdots p_k^{e_k}$, let's define \
$$f_1(n) = (p_1-1)^{e_1} (p_2-1)^{e_2} \cdots (p_k-1)^{e_k}.$$
For each integer $m \ge 2$, define recursively $f_m(n) = f_1(f_{m-1}(n))$. Determine for how many integers $N$ in the range $1 \leq N \leq 70$, the sequence $(f_1(N), f_2(N), f_3(N), \dots)$ is bounded.
A) 0
B) 5
C) 10
D) 15
E) 20

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