
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 \( f(x) = (x+3)^2 - 7 \). If the domain of \( f \) is all real numbers, then \( f \) does not have an inverse function. However, if we restrict the domain of \( f \) to an interval \([c, \infty)\), then \( f \) may have an inverse function. What is the smallest value of \( c \) we can use here, so that \( f \) does have an inverse function?

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