
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
Given the conditions of the previous problem, determine the work of adiabatic compression of a gas where its volume \(v\) and pressure \(p\) are related by the equation \(pv^{k}=c=\) const (Poisson's law), where \(k\) is a constant greater than one for the given gas. (For air, \(k \approx 1.4\)).

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