
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 five-game series between Team X and Team Y where the first team to win three games wins the series, and each team must win at least one game, and teams are equally likely to win each game. Team Y wins the third game and Team X wins the series, what is the probability that team Y also wins the first game?
A) $\frac{1}{3}$
B) $\frac{1}{2}$
C) $\frac{2}{3}$
D) $\frac{3}{4}$
E) $\frac{4}{5}$

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