
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

$$
f(x)=\left\{\begin{array}{l}
\frac{x^{2}+7 x+10}{x^{2}-4} \quad \text { for } \quad x<2, x \neq-2 \\
\frac{11}{4} \text { for } \quad x=-2 \\
4 x-3 \quad \text { for } \quad x \geqslant 2
\end{array}\right.
$$

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