
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
Let the function $f(x) = \log_{a}x$ ($a>0$, $a \neq 1$). If $f(x_1x_2\ldots x_{2008}) = 8$, what is the value of $f(x_1^2) + f(x_2^2) + \ldots + f(x_{2008}^2)$?

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