
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
Let  $c \ge 2$  be a fixed integer. Let  $a_1 = c$  and for all  $n \ge 2$  let  $a_n = c \cdot \phi (a_{n-1})$ . What are the numbers  $c$  for which sequence  $(a_n)$  will be bounded? $\phi$  denotes Euler’s Phi Function, meaning that  $\phi (n)$  gives the number of integers within the set  $\{1, 2, . . . , n\}$  that are relative primes to  $n$ . We call a sequence  $(x_n)$  bounded if there exist a constant  $D$  such that  $|x_n| < D$  for all positive integers  $n$ .

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