
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
Football is a very ancient sport, originating in China, and is the most influential single sport in the global sports world. Now, a random sample of footballs is selected to inspect the quality. The statistical results are as follows:

| Number of Footballs Selected $n$ | $100$ | $200$ | $400$ | $600$ | $1000$ | $1500$ | $2000$ |
|----------------------------------|-------|-------|-------|-------|--------|--------|--------|
| Number of High-Quality Items $m$ | $93$  | $192$ | $380$ | $561$ | $938$  | $1413$ | $1878$ |
| Frequency of High-Quality Items $\frac{m}{n}$ | $0.93$ | $0.96$ | $0.95$ | $0.935$ | $0.938$ | $0.942$ | $0.939$ |

Based on this, the estimated probability of randomly selecting a high-quality football from this batch is ____ (round the result to $0.01$).

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