
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 small weightless ring is hinged to a light rod of length \(2l\). Point masses of \(m\) and \(2m\) are fixed at the middle and end of the rod, respectively. The ring is placed on a smooth horizontal rod. Initially, the rod was held horizontally, and then it was released. Find the speed of the ring at the moment when the rod passes through the vertical position. Assume that the mass of the rod is zero.

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