
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
A square piece of paper has sides of length 120 cm. From each corner, a wedge is cut in the following manner: at each corner, the two cuts for the wedge start 12 cm from the corner, and they meet at an angle of 45 degrees. When the edges of each cut are folded to meet each other, they are taped together to form a cup shape with sides that are not perpendicular to the base. Determine the volume of the cup formed by assuming the sides form a perfect cone at each corner.

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