
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 masses, $m_{1}=1$ kg and $m_{2}=10$ kg, are placed on two horizontal shelves and are connected by a weightless and inextensible thread passing over a weightless smooth pulley. The coefficients of friction between the masses and the shelves are $\mu_{1}=0,3$ and $\mu_{2}=0,1$. A horizontally directed force $F=20$ N is applied to the center of the pulley. Determine the accelerations of the masses and the center of mass of this system. 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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