
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
A massless string is wrapped around a frictionless pulley of mass  $M$ . The string is pulled down with a force of 50 N, so that the pulley rotates due to the pull. Consider a point  $P$  on the rim of the pulley, which is a solid cylinder. The point has a constant linear (tangential) acceleration component equal to the acceleration of gravity on Earth, which is where this experiment is being held. What is the weight of the cylindrical pulley, in Newtons? 

*(Proposed by Ahaan Rungta)*

<details><summary>Note</summary>This problem was not fully correct. Within friction, the pulley cannot rotate. So we responded: 
<blockquote>Excellent observation! This is very true. To submit, I'd say just submit as if it were rotating and ignore friction. In some effects such as these, I'm pretty sure it turns out that friction doesn't change the answer much anyway, but, yes, just submit as if it were rotating and you are just ignoring friction. </blockquote>So do this problem imagining that the pulley does rotate somehow.</details>

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