
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 the function $$f(x)=a+\sin(x-\frac{1}{2})$$, if $$f(0)+f(\frac{1}{2019})+f(\frac{2}{2019})+…+f(\frac{2017}{2019})+f(\frac{2018}{2019})+f(1)=1010$$, find the value of the real number $a$.

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