
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 a positive integer  $k$ , let  $d(k)$  denote the number of divisors of  $k$  and let  $s(k)$  denote the digit sum of  $k$ . A positive integer  $n$  is said to be *amusing* if there exists a positive integer  $k$  such that  $d(k)=s(k)=n$ . What is the smallest amusing odd integer greater than  $1$ ?

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