
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

Half of the population of the island of Nevezhenia consists of hares, and all the rest are rabbits. If a resident of the island asserts something, he always sincerely believes what he is saying. At the same time, hares are mistaken in an average of every fourth case, whereas rabbits are mistaken in an average of every third case.

One day, an animal emerged in the center of the island and shouted: "I am not a hare!" Then thought for a moment and said sadly: "I am not a rabbit."

What is the probability that it actually is a hare?

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