
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 $\overrightarrow{a_{n}}=(\cos \frac {nπ}{3},\sin \frac {nπ}{3})$, $\overrightarrow{b}=(\cos θ,\sin θ)$, find the difference between the maximum and minimum values of $y=| \overrightarrow{a_{1}}+ \overrightarrow{b}|^{2}+| \overrightarrow{a_{2}}+ \overrightarrow{b}|^{2}+…+| \overrightarrow{a_{100}}+ \overrightarrow{b}|^{2}$.

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