
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 players face off in a dice combat game. The attacker will roll three dice and the defender will roll two. The attacker will defeat the defender in a single roll of dice if and only if both conditions below are satisfied:

i) The highest die of the attacker is greater than the highest die of the defender.

ii) The second highest die of the attacker is greater than the second highest die of the defender (we assume that the "second highest die" can be the same as the highest die if two or more dice tie for the highest value).

Given that all dice are fair and outcomes are equally probable, calculate the probability that the attacker wins when the defender rolls:

a) Two fives;

b) One five and one four.

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