
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 fox and two bear cubs are dividing 100 candies. The fox sorts the candies into three piles, and a draw determines who gets which pile. The fox knows that if the bear cubs end up with different amounts of candies, they will ask her to equalize their piles, and she will take the excess for herself. After that, everyone eats the candies they receive.

a) Devise a way for the fox to distribute the candies into piles so that she ends up eating exactly 80 candies (no more, no less).

b) Can the fox devise a way to end up eating exactly 65 candies?

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