
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 the crank-slider mechanism (1-crank, 2-connecting rod). These were first used in antiquity, in Roman sawmills. There, the rotation of the 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 $\omega=10\, \mathrm{rad/s}$. Find the equations of motion, the equation of the trajectory, and the velocity of point M on the connecting rod if $OA = AB = 90\, \mathrm{cm}$, and $AM = \frac{2}{3} AB$.

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