
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
Investigate the continuity and plot the graphs of the following functions:
1. \( f(x) = \begin{cases} 
3x & \text{if } x \neq 2 \\
1 & \text{if } x = 2 
\end{cases} \)
2. \( f(x) = \frac{x^2 - 16}{x - 4} \)
3. \( \varphi(x) = \begin{cases} 
x^2 & \text{if } x \leq 0 \\
x + 1 & \text{if } x > 0 
\end{cases} \)
5. \( f(x) = \frac{|x - 1|}{x - 1} \)

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