
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

...

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system
The force exerted by the airflow on the sail can be calculated using the formula

$$F=\frac{A S \rho\left(v_{0}-v\right)^{2}}{2}$$ 

where \(A\) is the aerodynamic force coefficient, \(S\) is the sail area (\(S = 4 \, \text{m}^{2}\)), \(\rho\) is the air density, \(v_{0}\) is the wind speed (\(v_{0} = 4.8 \, \text{m/s}\)), and \(v\) is the speed of the sailing vessel.

At a certain moment, the instantaneous wind power reaches its maximum value. What is the speed of the sailing vessel at this moment?

Given:

$$F=\frac{A S \rho\left(v_{0}-v\right)^{2}}{2}$$

\(N(t') = N_{\max}\)

\(v_{0} = 4.8 \, \text{m/s}\)

\(v(t') = ?\)

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