
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 function y=INT(x) is called the integer function, which means y is equal to the maximum integer not exceeding x, such as INT(0.89)=0, INT(2.90)=2. Given that a<sub>n</sub>\=INT($$\frac {1}{7}×2^{n}$$), b<sub>1</sub>\=a<sub>1</sub>, b<sub>n</sub>\=a<sub>n</sub>\-2a<sub>n-1</sub> (n∈N*, n≥2), find b<sub>2019</sub>.

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