
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
Antal numbers 100 matchboxes from 1 to 100 and puts an arbitrary number of matches in each box. Bea randomly selects 15 boxes, and Antal counts the matches in those boxes (without Bea seeing this) and tells her whether the total number of matches in the 15 boxes is even or odd. Bea can repeat this question step as many times as necessary. Can Bea determine if the number of matches in box number 1 is even or odd, and if so, what is the minimum number of steps required?

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