
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 number is divisible by 9 if the sum of its digits is divisible by 9. $C\,498\,DF4$ is divisible by 9 where $C, D,$ and $F$ each represent a single digit. What is the sum of all possible values of $C+D+F$?

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