
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
Calculate the following quotient without using a calculator or function table:

$$
\frac{\pi-\operatorname{arctg} \frac{8}{15}}{2 \cdot \operatorname{arctg} 4}
$$

Here, $\operatorname{arctg} x$ denotes the angle in the interval $\left(-\frac{\pi}{2} ; \frac{\pi}{2}\right)$ whose tangent is $x$.

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