
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
Jason rolls three fair standard six-sided dice and wins if and only if the sum of the numbers face up on the three dice is exactly $10$ after rerolling any subset of the dice, provided that he always plays to optimize his chances of winning. Determine the probability that Jason chooses to reroll exactly two of the dice.

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