
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 sequence ${a_n}$, it is known that $a_1 > 1$, $a_{n+1}=a_n^2-a_n+1 (n\in N^{*})$, and $\frac {1}{a_{1}}+ \frac {1}{a_{2}}+...+ \frac {1}{a_{2015}}=2$. Find the value of $a_1$ when $a_{2016}-4a_{1}$ takes the minimum value.

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