
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 2004 boxes on a table, each containing one ball. It is known that some of the balls are white, and their number is even. You are allowed to point to any two boxes and ask if there is at least one white ball among them. What is the minimum number of questions required to guarantee determining at least one box that contains a white ball?

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