
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
At the ends of a vertically aligned homogeneous spring, two small loads are attached. The load with mass \(m_{1}\) is at the top, and the load with mass \(m_{2}\) is at the bottom. A person holds the spring in the middle, maintaining it vertically in the air. In this scenario, the upper half of the spring is deformed by \(x_{1} = 8 \, \text{cm}\), and the lower half by \(x_{2} = 15 \, \text{cm}\). Subsequently, the person flips the spring, swapping the positions of the loads, and then places the spring on a horizontal surface and releases it. Determine the amount of deformation of the spring in this scenario. Neglect the size of the person's palm in comparison to the length of the spring.

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