
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 \( g(x) = (2x - 3)^2 - 4 \). Given that the domain of \( g \) includes all real numbers, \( g \) does not have an inverse function over all real numbers. However, by restricting \( g \)'s domain to an interval \([c, \infty)\), \( g \) can be invertible. Find the smallest value of \( c \) for which this is true.

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