
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 count is even. You are allowed to point at any two boxes and ask if there is at least one white ball in them. What is the minimum number of questions needed to guarantee the identification of at least two boxes containing white balls?

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