
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
Consider a crank-slider mechanism. (1-crank, 2-connecting rod). This type of mechanism was first used in antiquity, in Roman sawmills. There, the rotation of a wheel, driven by the force of falling water, was converted into the reciprocating motion of the saw blade. The given crank rotates with a constant angular velocity $\omega=10$ rad/s. Find the equations of motion, the equation of the trajectory, and the speed of point M of the connecting rod if $O A=A B=90 \mathrm{~cm}$, $A M=\frac{1}{2} A B$.

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