
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 rigid rod moves on a horizontal table. At a certain moment, the speed of one end of the rod is \( v_{1} = 10 \, \text{m/s} \), and the speed of the other end is \( v_{2} = 6 \, \text{m/s} \) directed along the axis of the rod. Determine the speed of the middle of the rod at this moment.

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