
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 middle school, in order to enrich students' extracurricular activities, has organized a series of cultural and sports activities, among which a 3-on-3 basketball competition is the most popular among students. There are two teams, Team A and Team B, participating in the competition. The probability of Team A winning each game is $\frac{1}{4}$, and there are no ties. Each game is independent of the others. <br/>$(1)$ If the competition adopts a best-of-three format, find the probability of Team A winning; <br/>$(2)$ If the competition adopts a best-of-five format, find the probability of Team B winning after the fourth game.

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