
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 rectangle with dimensions 20 units by 15 units, two congruent equilateral triangles are drawn such that each has one vertex on one corner of the rectangle. Calculate the side length of the largest square that can be inscribed in the space inside the rectangle and outside of the triangles assuming they meet at a point other than the corners.

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