
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 \( a, b \in \mathbf{R}^{+} \) and \( \frac{\sin^{4} x}{a} + \frac{\cos^{4} x}{b} = \frac{1}{a+b} \), determine \( \frac{\sin^{8} x}{a^{3}} + \frac{\cos^{8} x}{b^{3}} \).

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