
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 $a$ and $b$ are non-zero real numbers, and they satisfy the equation $\frac{a\sin \frac{\pi }{5}+b\cos \frac{\pi }{5}}{a\cos \frac{\pi }{5}-b\sin \frac{\pi }{5}}=\tan \frac{8\pi }{15}$, find the value of $\frac{b}{a}$.

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