
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
Given a function \( f \) defined over the domain \(\mathbf{R}\), which satisfies the equation \( f(x+2)[1-f(x)] = 1+f(x) \) with \( f(1) = 2 + \sqrt{2} \), find the value of \( f(1989) \).

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