
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
Inside a cylinder, there are two pairs of identical stops. The distance between the lower stops and the bottom is \( l_{1} = 10 \text{ cm} \), and the distance between the lower and upper stops is \( l_{2} = 15 \text{ cm} \). A piston with a maximum possible mass \( M = 10 \text{ kg} \), which these stops can support, lies on the lower stops. The area of the base of the cylinder is \( S = 10 \text{ cm}^2 \). What is the minimum amount of heat \( Q \) that should be transferred to a monoatomic ideal gas beneath the piston in order for the piston to be able to shoot out of the cylinder? The amount of gas beneath the piston is \( v = 1 \text{ mole} \), and its initial pressure is equal to atmospheric pressure \( p_{0} = 10^5 \text{ Pa} \). Neglect the thickness of the piston. The acceleration due to gravity is \( g = 10 \text{ m/s}^2 \).

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