
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 biologist wants to estimate the number of butterflies in a forest. On June 1, she catches a random sample of 100 butterflies, tags them, and releases them. On October 1, she catches a random sample of 80 butterflies and finds that 4 of them are tagged. To calculate the number of butterflies in the forest on June 1, she assumes that 30% of these butterflies are no longer in the forest on October 1 (due to death and emigrations), and that 50% of the butterflies were not in the forest on June 1 (due to births and immigrations), and that the number of untagged butterflies and tagged butterflies in the October 1 sample are representative of the total population. What does the biologist calculate for the number of butterflies in the forest on June 1?

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