
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 table tennis singles match between players A and B, the match is played in a best-of-seven format (i.e., the first player to win four games wins the match, and the match ends). Assume that both players have an equal chance of winning each game.  
(1) Calculate the probability that player B wins by a score of 4 to 1;  
(2) Calculate the probability that player A wins and the number of games played is more than 5.

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