
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 sum of the first 10 terms of a geometric sequence {a_n} is equal to a_{1}{(r^{9}-1)}/{(r-1)}, where r is the common ratio, given that a_2+a_4=10 and a_3^2=16. Find the value of log_{√2}(a_{1})+log_{√2}(a_{2})+log_{√2}(a_{3})+⋯+log_{√2}(a_{10}).

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