
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 late rice variety "San You No. 1" developed by the team of Yuan Longping, the "Father of Hybrid Rice," has a yield of $911.7$ kilograms per mu. Before this, the early rice variety planted in the same field had a yield of $619.06$ kilograms per mu. This means that the combined yield of the two seasons reached $1530.76$ kilograms per mu, achieving the goal of "1500 kilograms high yield breakthrough." In rice breeding, different traits of rice have different effects on its yield. A breeding research team measured the data of plant height (unit: cm) and panicle length (unit: plant) as shown in the table below:

|         | Long Panicle | Short Panicle | Total |
|---------|--------------|---------------|-------|
| Tall    | 34           | 16            | 50    |
| Short   | 10           | 40            | 50    |
| Total   | 44           | 56            | 100   |

$(1)$ Determine whether there is a relationship between plant height and panicle length with a probability of making an error not exceeding $0.01$.

$(2)$ In a sample of 50 short plants, 5 plants were further studied using stratified sampling with long and short panicles. From these 5 plants, 3 plants were selected to measure the total number of grains per panicle. Find the probability of having exactly one long panicle plant.

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