
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 the domain of the function f(x) is R, f(2x-2) is an even function, f(x-3)+f(-x+1)=0 when x∈[-2,-1], f(x)=\frac{1}{a^x}-ax-4 where a>0 and a≠1, and f(-2)=4, find Σ from k=1 to 19 of |f(k)|.

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