
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 two linear functions \( f(x) \) and \( g(x) \) such that the graphs \( y=f(x) \) and \( y=g(x) \) are parallel lines, but not parallel to the coordinate axes. Find the minimum value of the function \( (g(x))^2 - 3f(x) \), if the minimum value of the function \( (f(x))^2 - 3g(x) \) is \( \frac{11}{2} \).

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