
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
Several numbers are written on the board. It is allowed to erase any two numbers \( a \) and \( b \), and then write the number \( \frac{a+b}{4} \) in place of one of them. What is the smallest number that can remain on the board after 2018 such operations, if initially, there are 2019 units written on it?

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