
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
If $f(x)$ is defined for all integers $x \ge 0$, $f(1) = 1$, $f(2) = 3$, and
\[f(a + b) = f(a) + f(b) - 2f(a \cdot b)\] for all integers $a, b \ge 0$, compute $f(1986)$.

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