
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
Players $A$ and $B$ are playing a chess match under the following conditions: The winner is the first to reach (at least) 2 points; if they reach 2-2 points simultaneously, the match is a draw. (A win earns 1 point, a draw earns $1/2$ point, and a loss earns 0 points).

a) What is the expected number of games, given that the probability of a draw in each game is 0.5, and the probability of $A$ winning is 0.3?

b) What is the probability that $B$ wins the match?

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