
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 \( f(x) = x^{6} - 2 \sqrt{2006} x^{5} - x^{4} + x^{3} - 2 \sqrt{2007} x^{2} + 2 x - \sqrt{2006} \), then find \( f(\sqrt{2006} + \sqrt{2007}) \).

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