
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
The following table shows the data obtained by a biology interest group at a certain school when studying the germination rate of a plant seed under the same experimental conditions:

| Number of seeds in the experiment $n$ | $100$ | $200$ | $500$ | $1000$ | $2000$ | $5000$ |
|---------------------------------------|-------|-------|-------|--------|--------|--------|
| Number of germinated seeds $m$        | $94$  | $a$   | $475$ | $954$  | $1906$ | $4748$ |
| Germination rate $\frac{m}{n}$        | $0.94$| $0.955$ | $0.946$ | $b$ | $0.953$ | $0.9496$ |

$(1)$ In the table above, $a=$______, $b=$______;  
$(2)$ The estimated value of the probability that a randomly selected seed of this plant can germinate is ______ (rounded to $0.01$);  
$(3)$ If the school's labor base needs $9500$ seedlings of this plant, estimate how many seeds need to be prepared for germination and cultivation.

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