
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 car is moving at a constant speed \( v \) along a straight road. The motion is being tracked by a radar located at a distance \( h \) from the road. Determine the angular velocity and angular acceleration of the radar's rotatable antenna as a function of time and as a function of the angular displacement. Graph these functions, and determine at what angular displacement the angular acceleration is maximum.

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