
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
Express in terms of proportionality the formulas for centripetal acceleration:

$$
a=\frac{v^{2}}{r}=r \omega^{2}=\frac{4 \pi^{2} r}{T^{2}}
$$

where \(a\) denotes acceleration, \(v\) is the speed of the moving point, \(r\) is the radius of the circular trajectory, \(\omega\) is the angular velocity, and \(T\) is the period of revolution.

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