
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 wishes to estimate the fish population in a pond. On April 1, she captures and tags 50 fish, then releases them back into the pond. On August 1, she captures another sample of 80 fish and discovers that 4 of them are tagged. It is assumed that 30% of these fish have left the pond by August due to various reasons (like predation or out-migration), and 45% of the fish in August weren't in the pond in April (due to in-migration or new births). Assuming tag loss is negligible and the sample is representative, what is her estimate for the fish population in the pond on April 1?

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