
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 marine biologist is assessing the population of coral reef fishes in an area. On January 1, she captures and tags 100 fish before releasing them back into the ecosystem. On June 1, she then captures another sample of 150 fish, finding that 4 of these are tagged. She considers that 30% of the initial tagged fish might have left the area by June (due to environmental changes), and that 50% of the fish caught in June could be new juveniles not present in January. Estimate the fish population on January 1.

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