
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
There are two light springs of equal length but with different stiffnesses. The springs are placed vertically one on top of the other. A mass $m=100$ kg is placed on top. As a result, the construction is compressed by $x_{1}=12.5$ cm. After that, the springs are placed side by side and the same mass is placed on top again. In this case, the construction is compressed by $x_{2}=2$ mm. Find the stiffnesses of the springs. The acceleration due to gravity is $g=10\, \mathrm{m/s^2}$.

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