
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
Define $f(x)$ for all integers $x \geq 0$ where $f(1) = 2$, and for all integers $a, b \geq 0$,
\[f(a + b) = f(a) + f(b) - 2f(ab) + 1.\]
Compute $f(1986)$.

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