
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
To implement the fundamental task of cultivating morality and nurturing people, and adhere to the comprehensive development of quality education with the "five educations" in mind, a school advocates that parents guide their children to do some household chores at home. In order to understand the average weekly household labor time of ninth-grade students, a random sample of ninth-grade students was selected for a survey. Based on the survey results, the following frequency distribution table was drawn:

劳动时间$(x/时)$ | 频数（学生人数）
--- | ---
$0\leqslant x \lt 1$ | $8$
$1\leqslant x \lt 2$ | $20$
$2\leqslant x \lt 3$ | $7$
$3\leqslant x \lt 4$ | $5$

Please complete the following questions:

$(1)$ If there are a total of $400$ ninth-grade students, estimate that approximately ______ students spend less than $2$ hours on household chores per week.

$(2)$ In order to encourage students to do household chores, the school plans to select $2$ students from the participants of the survey to share their experiences. If only $2$ male students and $3$ female students with an average weekly household labor time of at least $3$ hours are randomly selected, please use a tree diagram or list method to calculate the probability that the two selected students consist of $1$ male student and $1$ female student.

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