
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 two sequences $\{a_n\}$ and $\{b_n\}$ satisfying $b_n=\log_{2}a_n$, where $n\in N_{+}$, and $\{b_n\}$ is an arithmetic sequence, and $a_9a_{2009}=4$, calculate the value of $b_1+b_2+b_3+\ldots+b_{2017}$.

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