
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
Two triangles - an equilateral triangle with side length \(a\) and an isosceles right triangle with legs of length \(b\) - are positioned in space such that their centers of mass coincide. Find the sum of the squares of the distances from all vertices of one triangle to all vertices of the other.

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