
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 with which the air stream acts on the sail can be calculated using the formula:

\[F=\frac{C S \rho\left(v_{0}-v\right)^{2}}{2}\]

where:
- \(C\) is the aerodynamic force coefficient,
- \(S\) is the area of the sail, given as \(S = 5 \, \text{m}^2\),
- \(\rho\) is the air density,
- \(v_0\) is the wind speed, given as \(v_0 = 6 \, \text{m/s}\),
- \(v\) is the speed of the sailboat.

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

Given:

\[F=\frac{CS \rho\left(v_{0}-v\right)^{2}}{2}\]

\[N\left(t^{\prime}\right)=N_{\max}\]

\[v_{0}=6 \, \text{m/s}\]

Find the speed \(v(t')\) at the time when the power is maximized.

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