
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 enhance the physical fitness of students and enrich the campus cultural and sports life, an eighth-grade basketball competition was held at a school in Fuchuan County. The competition was conducted in a round-robin format, meaning that each class had to compete in one match with every other class, totaling $45$ matches.  
$(1)$ How many classes are there in the eighth grade of the school?  
$(2)$ In the basketball competition, winning a game earns $2$ points, losing a game earns $1$ point. If Xiaofeng, a student in Class 2101, wants to score no less than $14$ points, how many victories does the class need to achieve at least?

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