
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 tree-planting group in a certain class plans to plant no less than $100$ trees this spring. If they plant 2 trees on the first day and the number of trees planted each subsequent day is double the number of the previous day, the minimum number of days $n\ (n\in \mathbb{N}^*)$ required is ____.

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