
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
There are 100 boxes numbered from 1 to 100. One of the boxes contains a prize, and the host knows where it is. The viewer can send the host a batch of notes with questions that require a "yes" or "no" answer. The host shuffles the notes in the batch and answers all of them honestly without announcing the questions out loud. What is the minimum number of notes that need to be sent to definitely find out where the prize is?

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