
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 airstream acts on a sail can be calculated using the formula:

\[ F = \frac{B S \rho (v_0 - v)^2}{2} \]

where \( B \) is the aerodynamic force coefficient, \( S \) is the sail area ( \( S = 7 \, \text{m}^2 \) ), \( \rho \) is the air density, \( v_0 \) is the wind speed ( \( v_0 = 6.3 \, \text{m/s} \) ), and \( v \) is the speed of the sailboat.

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

Given:

\[ F = \frac{B S \rho (v_0 - v)^2}{2} \]

\[ N(t') = N_{\text{max}} \]

\[ v_0 = 6.3 \, \text{m/s} \]

\[ v(t') = ? \]

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