
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
In a given diagram, there is an equilateral triangle with a side length of 10 m. Adjacent to it, there is a square each of whose sides is equal to the height of the equilateral triangle. Calculate the perimeter of the triangle and the area of the square.

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