
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 weightless cylindrical rollers lie on a horizontal surface parallel to each other and have radii \( R = 1 \) m and \( r = 40 \) cm. A flat heavy plate of mass \( m = 150 \) kg is placed on them so that it has an inclination to the horizon \( \alpha = \arccos(0.68) \). Find the magnitude and direction of the acceleration of the plate until the moment it touches the ground, assuming there is no slipping. What is the acceleration of the rollers? The acceleration due to gravity is \( 10 \, \mathrm{m/s}^2 \).

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