
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
For which values of \( x \) do the functions 1) \( y = \frac{1}{x} \), 2) \( y = \frac{3}{x+3} \), 3) \( y = \frac{x^{2}-1}{x^{2}+1} \), 4) \( y = \tan x \) have discontinuities? Provide additional examples of functions that are not continuous everywhere.

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