
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 with weights $m_1 = 2$ kg and $m_2 = 3$ kg are placed on two horizontal shelves. They are connected by a weightless, inextensible string that passes over a weightless, smooth pulley. The coefficients of friction between the masses and the shelves are $\mu_1=0.1$ and $\mu_2=0.2$ respectively. A horizontal force of $F=10$ N is applied to the center of the pulley. Determine the accelerations of the masses and the center of mass of this system of bodies. The acceleration due to gravity is $g=10 \ \mathrm{m/s^2}$.

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