
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  $A \text{ :}= \mathbb{Q}\setminus \{0,1\}$  denote the set of all rationals other than  $0$  and  $1$ .  A function  $f:A\to \mathbb{R}$  has the property that for all  $x\in A$ , \[f(x)+f\left(1-\dfrac{1}{x}\right)=\log |x|.\]  Compute the value of  $f(2007)$ .

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