
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 toy company undertakes the production task of the mascot dolls for the 19th Hangzhou Asian Games. A batch of dolls is randomly inspected, and the results are as follows:

| Number of dolls $n$ | $10$ | $100$ | $1000$ | $2000$ | $3000$ | $5000$ |
|---------------------|------|-------|--------|--------|--------|--------|
| Number of high-quality dolls $m$ | $9$ | $96$ | $951$ | $1900$ | $2856$ | $4750$ |
| Frequency of high-quality dolls $\frac{m}{n}$ | $0.9$ | $0.96$ | $a$ | $0.95$ | $0.952$ | $b$ |

Please answer the following questions based on the data in the table:
$(1)$ Fill in the blanks: $a=$______, $b=$______;
$(2)$ Estimate the probability that a randomly selected doll from this batch is a high-quality doll. (Round to $0.01$)

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