
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
Team A and team B play a series where the first team to win three games wins the series. Each team is equally likely to win each game, and there are no ties. The outcomes of the individual games are independent. If it is known that team B wins the third game and team A wins the series, what is the probability that team B wins the second game?
A) 1/2
B) 1/4
C) 1/3 
D) 1/5
E) 2/3

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