
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 the function f(x) = log<sub>m</sub>x (m > 0 and m ≠ 1), if m is the common ratio of the geometric sequence {a<sub>n</sub>}, and f(a<sub>2</sub>a<sub>4</sub>a<sub>6</sub>...a<sub>20</sub>) = 7, then the value of f(a<sub>1</sub><sup>2</sup>) + f(a<sub>2</sub><sup>2</sup>) + ... + f(a<sub>20</sub><sup>2</sup>) is ___.

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