
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
In a lake, lotuses grow. Each lotus splits into two in a day, so instead of one lotus there are two. After another day, each resulting lotus splits again, and so on. In 30 days, the lake is completely covered with lotuses. When was the lake half-covered?

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