
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
One of the boxes that Joshua and Wendy unpack has Joshua's collection of board games.  Michael, Wendy, Alexis, and Joshua decide to play one of them, a game called  $\textit{Risk}$  that involves rolling ordinary six-sided dice to determine the outcomes of strategic battles.  Wendy has never played before, so early on Michael explains a bit of strategy.

"You have the first move and you occupy three of the four territories in the Australian continent.  You'll want to attack Joshua in Indonesia so that you can claim the Australian continent which will give you bonus armies on your next turn."

"Don't tell her  $\textit{that!}$ " complains Joshua.

Wendy and Joshua begin rolling dice to determine the outcome of their struggle over Indonesia.  Joshua rolls extremely well, overcoming longshot odds to hold off Wendy's attack.  Finally, Wendy is left with one chance.  Wendy and Joshua each roll just one six-sided die.  Wendy wins if her roll is  $\textit{higher}$  than Joshua's roll.  Let  $a$  and  $b$  be relatively prime positive integers so that  $a/b$  is the probability that Wendy rolls higher, giving her control over the continent of Australia.  Find the value of  $a+b$ .

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