
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 certain type of rice seed germination experiment under the same conditions yielded the following results:

| Number of seeds per batch $m$ | $100$ | $500$ | $800$ | $1000$ | $2000$ | $5000$ |
|-------------------------------|-------|-------|-------|--------|--------|--------|
| Number of germinations $n$     | $94$  | $442$ | $728$ | $902$  | $1798$ | $4505$ |
| Germination rate $\frac{n}{m}$ | $0.940$ | $0.884$ | $0.910$ | $a$ | $0.899$ | $0.901$ |

$(1)$ The value of $a$ in the table is ________;<br/>$(2)$ The estimated value of the germination probability of this type of rice seed is ________ (rounded to $0.1$);<br/>$(3)$ Using the estimated value of the probability in $(2)$, estimate how many kilograms of germinable seeds are in $10$ kilograms of this type of rice seed?

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