
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
Given that functions \( f(x)=x^{2}+r x+s \) and \( g(x)=x^{2}-9 x+6 \) have the properties that the sum of roots of \( f(x) \) is the product of the roots of \( g(x) \), and the product of roots of \( f(x) \) is the sum of roots of \( g(x) \). If \( f(x) \) attains its minimum at \( x=a \), find the value of \( a \).

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