
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 {a_n} is an arithmetic sequence, with the first term a_1 > 0, a_{2013} + a_{2014} > 0, and a_{2013} \cdot a_{2014} < 0, calculate the largest natural number n for which the sum of the first n terms S_n > 0.

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