
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 die is tossed repeatedly. Player A wins if a 1 or 2 appears on two consecutive tosses. Player B wins if a 3, 4, 5, or 6 appears on two consecutive tosses. Find the probability of each player winning if the die is tossed at most 5 times. Also, determine the probability of each player winning if the die is tossed until a player wins.

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