
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
A batch of shirts is inspected, and the frequency table of qualified shirts is as follows:

| Number of Shirts Inspected | $50$ | $100$ | $200$ | $500$ | $800$ | $1000$ |
|----------------------------|------|-------|-------|-------|-------|--------|
| Frequency of Qualified Shirts | $47$ | $95$ | $188$ | $480$ | $763$ | $949$ |
| Frequency Rate of Qualified Shirts | $0.94$ | $0.95$ | $0.94$ | $0.96$ | $0.95$ | $0.95$ |

$(1)$ Estimate the probability of randomly selecting a qualified shirt (round the result to $0.01$).<br/>$(2)$ Estimate the number of defective shirts out of $2000$ shirts sold.

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