
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
Evaluate:
$(1)\ [(-1+i)\cdot i^{100}+( \frac {1-i}{1+i})^{5}]^{2017}-( \frac {1+i}{ \sqrt {2}})^{20}$
$(2) \ \int_{-1}^{1}\[3\tan x+\sin x-2x^{3}+ \sqrt {16-(x-1)^{2}}\]dx\cdot$

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