
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
The sequence $b_1, b_2, \ldots$ is geometric with $b_1=b$ and common ratio $s,$ where $b$ and $s$ are positive integers. Given that $\log_4 b_1+\log_4 b_2+\cdots+\log_4 b_{10} = 2010,$ find the number of possible ordered pairs $(b,s).$

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