
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
(1) Given vectors $\overset{→}{a}=(1,-3)$, $\overset{→}{b}=(-2,6)$, if vector $\overset{→}{c}$ forms an angle of $60^{\circ}$ with $\overset{→}{a}$, and $\overset{→}{c}·(\overset{→}{a}+\overset{→}{b})=-10$, then $|\overset{→}{c}|=$______.

(2) Given a sequence $\{a_n\}$ that satisfies $a_1=1, a_2=0, a_{n+2}=a_{n+1}-a_n (n\geqslant 1)$, then $a_{2017}=$______.

(3) Given real numbers $x > 0$, $y > 0$, and satisfying $x+y=1$, then the minimum value of $\frac{2}{x}+ \frac{x}{y}$ is ______.

(4) Given a right prism $ABC-A_1B_1C_1$ with $AB=3$, $AC=4$, $AB⊥AC$, $AA_1=2$, then the sum of the surface areas of the inscribed and circumscribed spheres of the prism is ______.

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