
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
During measurement, due to errors from measuring instruments and human observation, the obtained data can have discrepancies from the true values, providing only approximate values. For multiple measured data points \(a_{1}, a_{2}, \cdots, a_{n}\), it is common to calculate their "best approximation value" \(x\) (the best approximation value \(x\) minimizes the sum of the squares of the differences between \(x\) and the \(n\) approximate data points \(a_{1}, a_{2}, \cdots, a_{n}\)). Determine this "best approximation value" \(x= \qquad\).

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