
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) during the isothermal compression of the gas by a piston that has moved inside the cylinder by $h$ meters.

Hint: The equation of state for the gas is given by $\rho V=$ const, where $\rho$ is pressure and $V$ is volume.

Given:
$$
H=0.4 \text{ m}, \ h=0.2 \text{ m}, \ R=0.1 \text{ m}
$$

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