
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 crank rotates with a constant angular velocity $\omega=10$ rad/s. Find the equations of motion, the equation of the trajectory, and the velocity of point \( M \) on the rod, given \( OA=AB=90 \text{ cm} \) and \( AM=\frac{2}{3} AB \).

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