
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 different numbers are randomly selected from the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$. The probability that their sum is 14 would be greater if the number $n$ had first been removed from the set $S$. What is the value of $n$?

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