
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
Lucía multiplies some positive one-digit numbers (not necessarily distinct) and obtains a number  $n$  greater than 10. Then, she multiplies all the digits of  $n$  and obtains an odd number. Find all possible values of the units digit of  $n$ . $\textit{Proposed by Pablo Serrano, Ecuador}$ 

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