
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
Inside a square with side length 15, two congruent equilateral triangles are drawn such that each has one vertex on a corner of the square and the opposite side is parallel to the side of the square. Each triangle shares one side with the square. What is the side length of the largest square that can be inscribed in the space inside the square but outside of the triangles?

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