
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 on the island of Misfortune are hares, and the rest are rabbits. If a resident of the island of Misfortune makes a statement, they always sincerely believe in what they say. However, hares are wrong on average in every fourth case, while rabbits are wrong on average in every third case. One day, a creature came to the center of the island and shouted: "I am not a hare!". Then it thought and sadly said: "I am not a rabbit". What is the probability that the creature is actually a hare?

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