
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
Two identical vessels of height \(H\) are connected by a thin tube with a valve \(K\) at a height of \(0.15H\). The left vessel is filled with water, and the right vessel is filled with gasoline. The liquid levels are the same and equal to \(0.9H\). Determine the levels of the liquids in the vessels after opening the valve. The density of water is 1000 kg/m³ and the density of gasoline is 600 kg/m³.

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