
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 edges of a rectangular prism are 26, 20, and 8 units long. Build straight gable roofs above the $26 \times 8$-us faces, where the "slanted" edges are 13 units long, and the "horizontal" edge is 20 units long. What is the volume of the part of the rectangular prism obtained by removing the mirror images, with respect to the faces to which the roofs are attached, of the roofs from the prism?

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