
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
A list of five positive integers has all of the following properties:

- The only integers in the list that occurs more than once are $9$ and $7$, each exactly twice.
- The median is $12$, 
- Its average (mean) is $15$.

What is the largest possible integer that could appear in the list?

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