
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]


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Solve the problem using as many different methods as possible. Methods are considered different if they use different mathematical ideas or distinct technical implementations of the same idea. Indicate the place of each method used in the school mathematics curriculum.

Find the range of the function \( f(x) = x - 1 + \sqrt{6x - x^2} \).

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