
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 estimates the number of fish in a lake using the capture-recapture technique. First, on April 1, 100 fish are tagged and released. After four months (i.e., on August 1), another sample of 100 fish is caught, of which 5 are found to be tagged. The biologist assumes that 30% of the fish initially tagged either died or migrated out of the lake by August, and that 20% of the captured fish in August are newcomers (either born or migrated in after April 1). Estimate the total number of fish in the lake at the beginning of April.

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