
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
The height of a right frustum of a cone is $m=\frac{3}{\pi} \mathrm{dm}$, and the inclination angle of the slant height is $\alpha=43^{\circ} 40^{\prime} 42.2^{\prime \prime}$. What is the volume of this frustum if the volume of the complete cone is $k=1 \mathrm{~m}^{3}$?

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