
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
Suppose that \( f(x)=\frac{2x+1}{x-2} \) and that \( y=g(x) \) is a linear function. If \( f^{-1}(g(2))=7 \) and \( g^{-1}(f(1))=\frac{4}{5} \), what is the \( x \)-intercept of \( y=g(x) \)?

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