
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 $150$. From each corner, a wedge is cut such that the two cuts each start at a distance $5$ from the corner, and they meet on the diagonal at an angle of $45^{\circ}$. The paper is then folded up along the lines joining the vertices of adjacent cuts, and when the two edges of a cut meet, they are taped together. Calculate the height of the tray formed, i.e., the perpendicular distance between the base and the plane formed by the upper edges.

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