
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
A cylinder is filled with gas at atmospheric pressure (103.3 kPa). Assuming the gas is ideal, determine the work (in joules) done during the isothermal compression of the gas by a piston that moves inward by \( h \) m.

Hint: The equation of state for the gas is

\[ \rho V = \text{const} \]

where \( \rho \) is the pressure and \( V \) is the volume.

\[ H = 0.8 \text{ m}, \, h = 0.7 \text{ m}, \, R = 0.2 \text{ m} \]

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