
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 small weights are attached to the ends of a vertically oriented uniform spring. The weight with mass $m_{1}$ is on the top, and the weight with mass $m_{2}$ is at the bottom. A person grasps the middle of the spring and holds it vertically in the air. As a result, the upper half of the spring is deformed by $x_{1} = 8 \, \text{cm}$, and the lower half by $x_{2} = 15 \, \text{cm}$. Then, without inverting it, the person places the spring on a horizontal surface and releases it. Determine the deformation of the spring in this case. Neglect the size of the person's hand compared to the length of the spring.

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