
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 person arrives in a city with very interesting news and informs two people about it in 10 minutes. Each of those who learn the news informs two more people (who do not yet know it) in another 10 minutes, and so on. How long will it take for the entire city, which has three million inhabitants, to know the news?

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