
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 school focuses on curriculum development and has established a student labor practice base. They have developed agricultural labor courses, conducted extracurricular planting and breeding activities, and plan to introduce small animal A and establish a breeding group. In order to understand the students' willingness to breed, the school conducted a survey among 100 first-year students, and the survey data is shown in the table below:

| Gender | Like breeding small animal A | Dislike breeding small animal A |
|--------|------------------------------|---------------------------------|
| Male   | 20                           | 30                              |
| Female | 40                           | 10                              |

$(1)$ Estimate the probabilities of male and female students in the school who like breeding small animal A.  
$(2)$ The school decides to have the first-year students responsible for breeding small animal A. They randomly select 6 students who like small animal A using stratified random sampling to form a breeding group. From these 6 students, 2 students are randomly selected to be the main responsible persons of the breeding group. Find the probability that these 2 students are both female.

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