
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 Go game competition between two players, A and B, it is agreed that the first to win 3 games will be declared the winner of the competition, and the competition will end. Assuming in a single game, the probability of A winning is 0.6, and the probability of B winning is 0.4, with the results of each game being independent of each other. It is known that in the first 2 games, A and B each won one game.  
(1) Find the probability of A winning the competition;  
(2) Find the probability that the competition ends after 5 games.

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