
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
The force exerted by the airflow on a sail can be calculated using the formula \( F = \frac{c s \rho (v_{0} - v)^{2}}{2} \), where \( C \) is the aerodynamic force coefficient, \( S \) is the sail area, \( \rho \) is the air density, \( v_{0} \) is the wind speed, and \( v \) is the speed of the sailboat. At a certain point in time, the instantaneous power of the wind reaches its maximum value. What is the speed of the sailboat at this moment?

Given:
\[ F = \frac{c s \rho (v_{0} - v)^{2}}{2} \]
\[ N(t') = N_{\max} \]
\[ v_{0} \]
\[ \overline{v(t') - ?} \]

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