
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
For any \( x \in \mathbf{R} \), the function \( f(x) \) satisfies the equation \( f(x+2008) = f(x+2007) + f(x+2009) \) and given that \( f(1) = \log \frac{3}{2} \) and \( f(2) = \log 15 \), what is the value of \( f(2007) \)?

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