
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
In measurements, in order to determine the best value of the object being measured, it is often necessary to measure the same object several times, and then select the number that minimizes the sum of the squares of the differences between each measurement data as the best approximate value. For example, after measuring the lengths of 5 barley spikes, the data obtained are 6.5, 5.9, 6.0, 6.7, and 4.5. Then, the best approximate length of these barley spikes can be obtained by finding the value of $x$ that minimizes the function $y=(x-6.5)^{2}+(x-5.9)^{2}+(x-6.0)^{2}+(x-6.7)^{2}+(x-4.5)^{2}$. Simplify the above expression and find the best approximate length of the barley spikes.

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