
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
In a horizontal stationary cylindrical vessel closed by a piston of mass \( M \), there is gas. The gas is heated for a time period \(\tau\), during which the piston moves from rest with a constant acceleration \(a\). Find the average power of the heater. The internal energy of one mole of gas is \( U = cT \). Neglect the heat capacity of the vessel and piston. The outer side of the piston is in a vacuum.

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