
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
In the geometric sequence {a<sub>n</sub>}, all terms are positive, and a<sub>10</sub>a<sub>11</sub>+a<sub>8</sub>a<sub>13</sub>=64. Find the value of log<sub>2</sub>a<sub>1</sub>+log<sub>2</sub>a<sub>2</sub>+…+log<sub>2</sub>a<sub>20</sub>.

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