
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
Given that the number of rabbits in a farm increases such that the difference between the populations in year $n+2$ and year $n$ is directly proportional to the population in year $n+1$, and the populations in the years $2001$, $2002$, and $2004$ were $50$, $80$, and $170$, respectively, determine the population in $2003$.

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