
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
The rules of table tennis competition stipulate: In a game, before the opponent's score reaches a tie at 10, one side serves twice consecutively, then the other side serves twice consecutively, and so on. Each serve, the winning side scores 1 point, and the losing side scores 0 points. Assume in a match between player A and player B, each time A serves, the probability of A scoring 1 point is 0.6, and the outcomes of each serve are independent. In a game between A and B, with A serving first:
1. Find the probability that the score is 1:2 in favor of B by the time the fourth serve starts.
2. Find the probability that A is leading in score by the time the fifth serve starts.

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