
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-rod). The first uses of these mechanisms appeared in antiquity, in Roman sawmills where the rotation of a wheel driven by falling water was converted into the reciprocating motion of a saw blade. The given crank rotates with a constant angular velocity of $\omega=10$ rad/s. Find the equations of motion, the equation of the trajectory, and the velocity of point M of the rod if $O A=A B=90 \text{ cm}, A M=\frac{2}{3} A B$.

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