
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

The vertices of the quadrilateral \( A_{1} A_{2} A_{3} A_{4} \) (Fig. 62) have the following masses placed respectively: \(2, 6, 2, 3\). Compute the moment of inertia of the resulting system of point masses relative to point \( S \). (The side length of each small square in Fig. 62 is equal to 1 unit.)

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