
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
To estimate the number of fish in the lake, $100$ fish were caught and marked, then released back into the lake. After a while, when the marked fish had mixed with the rest of the fish, a second catch was made of $200$ fish, of which $25$ were found to be marked. We can estimate that there are $\_\_\_\_\_\_$ fish in the lake $(.)$

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