
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
Five six-sided dice are rolled. It is known that after the roll, there are two pairs of dice showing the same number, and one odd die. The odd die is rerolled. What is the probability that after rerolling the odd die, the five dice show a full house?

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