
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 best-of-three (race to two wins) billiards match between players A and B, it is known that the probability of player A winning any given game is 0.6 and the probability of player B winning is 0.4. What is the probability that player B will ultimately win the match?

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