
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
Rob is helping to build the set for a school play.  For one scene, he needs to build a multi-colored tetrahedron out of cloth and bamboo.  He begins by fitting three lengths of bamboo together, such that they meet at the same point, and each pair of bamboo rods meet at a right angle.  Three more lengths of bamboo are then cut to connect the other ends of the first three rods.  Rob then cuts out four triangular pieces of fabric: a blue piece, a red piece, a green piece, and a yellow piece.  These triangular pieces of fabric just fill in the triangular spaces between the bamboo, making up the four faces of the tetrahedron. The areas in square feet of the red, yellow, and green pieces are  $60$ ,  $20$ , and  $15$  respectively. If the blue piece is the largest of the four sides, find the number of square feet in its area.

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