
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
A very thin and homogeneous rod is standing in a vertical position on a horizontal surface. The rod falls over without initial velocity. Calculate the angular acceleration of the rod as a function of the angle between the rod and the horizontal plane. What is the angular velocity of the rod when it hits the ground? Friction between the rod and the surface is negligible.

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