
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). They were first used in antiquity in Roman sawmills, where the rotation of a wheel driven by falling water was converted into the reciprocating motion of the saw blade. This 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 connecting rod, given $O A = A B = 90 \, \text{cm}$, and $A M = \frac{1}{2} A B$.

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