
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
Compute the following expressions:

(1) $\frac{2+2i}{(1-i)^2} + \left(\frac{\sqrt{2}}{1+i}\right)^{2010}$;

(2) $(4-i^5)(6+2i^7) + (7+i^{11})(4-3i)$.

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