
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 \(\tan \alpha\) and \(\tan \beta\) be two solutions of the equation \(x^{2}-3x-3=0\). Find the value of
$$
\left|\sin^2(\alpha+\beta) - 3 \sin(\alpha+\beta) \cos(\alpha+\beta) - 3 \cos^2(\alpha+\beta)\right|.
$$
(Note: \(|x|\) denotes the absolute value of \(x\).)

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