
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 sealed horizontal cylindrical vessel of length \( l \) is divided into two parts by a movable partition. On one side of the partition, there is 1 mole of oxygen, and on the other side, there is 1 mole of helium and 1 mole of oxygen, with the partition being initially in equilibrium. At a certain moment, the partition becomes permeable to helium but remains impermeable to oxygen. Find the displacement of the partition. The temperatures of the gases are the same and do not change during the process.

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