
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
Consider a quadratic function \( g(x) = 3x^2 - 9x + 2 \). By restricting the domain of this function to an interval, it can be made invertible. What is the largest such interval that includes the point \( x = 1 \)?

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