
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
Given the functions y = 3 - x, y = 1/(x^2 + 1), y = x^2 + 2x - 10, and y = \begin{cases} -x & (x \leq 0) \\ -\frac{1}{x} & (x > 0) \end{cases}, determine the number of functions whose range is the set of all real numbers.

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