
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
How to determine the number of fish in a pond?

We catch \( n_{a} = 20 \) fish, mark them, and release them back into the pond. After some time, enough for the marked fish to distribute themselves evenly throughout the pond, we catch \( m = 50 \) fish. Suppose among them, \( k_{1} = 7 \) are marked. Determine the number of fish in the pond \( N \) using the maximum likelihood method.

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