
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 \( f \) be a function such that
\[ 
f(x) - \frac{1}{2} f\left(\frac{1}{x}\right) = \log x 
\]
for all \( x > 0 \), where \( \log \) denotes the logarithm base 10. Find \( f(1000) \).

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