
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 complex numbers $z_{1}=a-2i$ and $z_{2}=3+4i$ ($a\in\mathbb{R}$, $i$ is the imaginary unit).

(1) If $z_{1}\cdot z_{2}$ is a pure imaginary number, find the value of the real number $a$;

(2) If the point corresponding to the complex number $z_{1}\cdot z_{2}$ in the complex plane is in the fourth quadrant, find the range of values for the real number $a$.

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