
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 a sequence of vectors $\overrightarrow{a\_1}, \overrightarrow{a\_2}, ..., \overrightarrow{a\_n}, ...$ arranged in order, if $\overrightarrow{a\_1}=(-2014,13)$ and $\overrightarrow{a\_n}-\overrightarrow{a\_{n-1}}=(1,1)$, find the serial number $n=$______ of the vector with the smallest magnitude.

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