
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. A prize is hidden in one of the boxes, and the host knows its location. 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, without announcing the questions aloud, honestly answers all of them. What is the minimum number of notes that need to be sent to definitely determine where the prize is located?

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