
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
Exactly half of the population of the island Nevezennya are hares, and all the others are rabbits. If an inhabitant of the island Nevezennya states something, they always sincerely believe in what they are saying. However, hares earnestly make mistakes on average in one out of every four cases, while rabbits earnestly make mistakes on average in one out of every three cases. One day, a creature came to the center of the island and shouted: "I am not a hare!". It thought for a moment and sadly said: "I am not a rabbit." What is the probability that it is indeed a hare?

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