
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
You have a keyring with \( n \) identical keys. You want to color code the keys so that each key is distinguishable from the others. What is the minimum number of colors required?

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