
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 that $\tan(2\theta) = -2$ with $\pi < 2\theta < 2\pi$.

(1) Find the value of $\tan(\theta)$;

(2) Find the value of $\sin^4(\theta) - \cos^4(\theta)$.

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