
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 \( r = 50 \) cm. A heavy flat plate with mass \( m = 75 \) kg is placed on them so that it is inclined to the horizon at an angle \( \alpha = \arccos(0.82) \). Find the magnitude and direction of the plate's acceleration until it touches the ground, assuming no slipping occurs. What is the acceleration of the rollers? The acceleration due to gravity is \( 10 \, \text{m/s}^2 \).

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