
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
In a basketball shooting competition for teachers at a certain school, the rules are: each round consists of shooting 6 balls, and the player wins if at least 4 balls are shot successfully and the last 2 balls are both successful; otherwise, the player loses. Given that the probability of teacher A shooting each ball successfully is $\frac{2}{3}$, find the probability that teacher A wins in one round.

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