
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
In the arithmetic sequence $\{a_{n}\}$ with common difference $d > 0$, $a_{2009}$ and $a_{2010}$ are the roots of the equation $x^{2}-3x-5=0$. $S_{n}$ is the sum of the first $n$ terms of the sequence $\{a_{n}\}$. Determine the smallest natural number $n$ that satisfies $S_{n} > 0$.

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