
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
Two teams, Team A and Team B, are playing in a basketball finals series that uses a "best of seven" format (the first team to win four games wins the series and the finals end). Based on previous game results, Team A's home and away schedule is arranged as "home, home, away, away, home, away, home". The probability of Team A winning at home is 0.6, and the probability of winning away is 0.5. The results of each game are independent of each other. Calculate the probability that Team A wins the series with a 4:1 score.

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