
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
Given the frequency of high-quality table tennis balls in a sample of size $50$ is $0.900$, in a sample of size $100$ is $0.920$, in a sample of size $200$ is $0.970$, in a sample of size $500$ is $0.948$, in a sample of size $1000$ is $0.951$, and in a sample of size $2000$ is $0.950$, calculate the approximate probability of randomly selecting a high-quality table tennis ball.

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