
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 of the function

$$
f(x)=\left\{\begin{array}{lll}
\frac{e^{1 / x}}{} & \text { for } & x<0 \\
\frac{x^{2}+7 x}{x^{2}+19} & \text { for } & 0 \leqslant x \leqslant 1 \\
\frac{4 x+2}{x^{2}-1} & \text { for } & x>1
\end{array}\right.
$$

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