
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 barrel with a height of 1.5 meters is completely filled with water and sealed with a lid. The mass of the water in the barrel is 1000 kg. A long, thin vertical tube with a cross-section of $1 \mathrm{~cm}^{2}$ is inserted into the lid of the barrel and completely filled with water. Find the length of the tube if it is known that after filling, the pressure at the bottom of the barrel increased by 2 times. The density of water is 1000 kg/m³.

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