
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
Two mathematicians, Kelly and Jason, play a cooperative game. The computer selects some secret positive integer  $ n < 60$  (both Kelly and Jason know that  $ n < 60$ , but that they don't know what the value of  $ n$  is). The computer tells Kelly the unit digit of  $ n$ , and it tells Jason the number of divisors of  $ n$ . Then, Kelly and Jason have the following dialogue:

Kelly: I don't know what  $ n$  is, and I'm sure that you don't know either. However, I know that  $ n$  is divisible by at least two different primes.

Jason: Oh, then I know what the value of  $ n$  is.

Kelly: Now I also know what  $ n$  is.

Assuming that both Kelly and Jason speak truthfully and to the best of their knowledge, what are all the possible values of  $ n$ ?

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