
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
The mass of a vessel completely filled with kerosene is 31 kg. If the vessel is completely filled with water, its mass will be 33 kg. Determine the mass of the empty vessel. The density of water $\rho_{B}=1000 \, \mathrm{kg} / \mathrm{m}^{3}$, and the density of kerosene $\rho_{K}=800 \, \mathrm{kg} / \mathrm{m}^{3}$.

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