
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 turtles in a pond. On June 1, she captures 80 turtles, tags them, and releases them back into the pond. On October 1, she captures another random sample of 50 turtles and finds that 2 of them are tagged. To calculate the number of turtles in the pond on June 1, she assumes that 20% of these turtles are no longer in the pond on October 1 (due to predation or migration), and that 30% of the turtles were not in the pond on June 1 (due to births and immigrations). She also assumes that the October 1 sample is representative of the total population. What does the biologist calculate for the number of turtles in the pond on June 1?

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