
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 $f(x)$ be defined for all integers $x \geq 0$, with $f(1) = 1$, and
\[f(a + b) = f(a) + f(b) - 2f(ab) + 1\] for all integers $a, b \geq 0$. Determine the value of $f(1986)$.

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