
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 air density is \( 1.2 \) kg/m\(^3\), constant pressure \( P \) is related to air density \( \rho \), area \( A \), and the square of the wind velocity \( V \) by the equation \( P = \rho kAV^2 \). Given that \( P = 0.75 \) pounds when \( A = 2 \text{ ft}^2 \) and \( V = 12 \text{ mph} \), determine the wind velocity \( V \) in miles per hour when \( P = 20.4 \) pounds and \( A = 10.764 \text{ m}^2 \).

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