
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 basketball team plays against 6 other teams in a series of 6 games, with each game resulting in a win or loss. Assume that the events of winning against the other teams are independent, and the probability of winning is $\dfrac{1}{3}$.  
(1) Find the probability that this team loses two games before winning for the first time;  
(2) Find the probability that this team wins exactly 3 out of the 6 games;  
(3) Find the expected number of wins and the variance of wins for this team in the 6 games.

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