
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. The results of a random inspection of a batch of dolls are as follows. Please answer the questions based on the data in the table:<br/>

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

$(1)$ $a=$______; $b=______$.<br/>
$(2)$ The estimated probability of randomly selecting $1$ high-quality doll from this batch of dolls is ______. (Round to $0.01$)<br/>
$(3)$ If the company produces $10000$ dolls in this batch, approximately how many high-quality dolls are in this batch?

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