
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
In a laboratory, there are flasks of two sizes (volume $V$ and volume $V / 2$) in a total quantity of 100, with at least three of each size. A lab technician randomly selects three flasks in succession. The first flask is filled with an 80% salt solution, the second with a 50% salt solution, and the third with a 20% salt solution. The contents of these three flasks are then poured into one container, and the salt percentage in this container is determined. For what minimum number of large flasks $N$ will the event "the salt percentage in the container is between 45% and 55% inclusive" occur less frequently than the event "when two fair coins are tossed, one shows heads and the other shows tails (in any order)"? Justify your answer. (16 points)

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