
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
Let \( a > 0 \). The function \( f(x) = x + \frac{100}{x} \) attains its minimum value \( m_{1} \) on the interval \( (0, a] \), and its minimum value \( m_{2} \) on the interval \( [a, +\infty) \). If \( m_{1} m_{2} = 2020 \), find the value of \( a \).

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