
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
Given the numbers: one and nine zeros. It is allowed to select two numbers and replace each with their arithmetic mean. What is the smallest number that can appear in place of the one after a series of such operations?

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