
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
Team A and Team B are playing in the basketball finals, with the rules being a best-of-seven series, meaning the first team to win four games wins the championship. If Team A has a 0.6 probability of winning each game, with each game having a definite winner and the outcome of each game not affecting the next,  
(1) Calculate the probability of Team A winning the championship after the fifth game;  
(2) Calculate the probability of Team A winning the championship overall;

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