
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 Unlucky Island are hares, and the rest are rabbits. If a resident of Unlucky Island makes a statement, they always sincerely believe what they are saying. However, hares earnestly mislead on average in every fourth case, and rabbits earnestly mislead on average in every third case. One day, an animal 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 it is actually a hare?

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