
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
A table tennis singles match is held between two players, Player A and Player 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 each player has an equal chance of winning each game.  
(1) Find the probability that Player A wins with a score of 4 to 1;  
(2) Find the probability that Player B wins and the match lasts more than 5 games;  
(3) Find the distribution of the number of games played.

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