
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 base of a right prism is a right triangle with a hypotenuse of length \( c \) and an acute angle of \( 30^\circ \). A plane is drawn through the hypotenuse of the lower base and the right angle vertex of the upper base, forming an angle of \( 45^\circ \) with the plane of the base. Determine the volume of the triangular pyramid that is cut off from the prism by this plane.

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