
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
Let $\overrightarrow{a_{1}}, \overrightarrow{a_{2}}, \ldots, \overrightarrow{a_{n}}, \ldots$ be a sequence of vectors arranged in order. Given $\overrightarrow{a_{1}} = (-2014, 13)$, and $\overrightarrow{a_{n}} - \overrightarrow{a_{n-1}} = (1, 1)$, find the index $n$ of the vector with the smallest magnitude.

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