
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 \( f(x) = \log_a x \) where \( a > 0 \) and \( a \neq 1 \). If \( f(x_1 x_2 \cdots x_{2003}) = 8 \), determine the value of \( f(x_1^2) + f(x_2^2) + \cdots + f(x_{2003}^2) \).

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