
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 under atmospheric pressure (103.3 kPa). Assuming the gas is ideal, determine the work (in joules) done in an isothermal compression of the gas by a piston moving inward by $h$ meters.

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

Given:
\[ H = 1.6 \text{ m}, \ h = 1.4 \text{ m}, \ R = 0.3 \text{ m} \]

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