
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 3000 positive integers has a unique mode, which occurs exactly 15 times. Apart from this, one number occurs exactly 14 times. Determine the least number of distinct values that can occur in the list.

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