
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 $z_{1}=a+2i$, $z_{2}=3-4i$ ($a\in\mathbb{R}$, $i$ is the imaginary unit).  
(I) If $z_{1}\cdot z_{2}$ is a pure imaginary number, find the value of the real number $a$;  
(II) If the complex number $z_{1}\cdot z_{2}$ corresponds to a point in the second quadrant on the complex plane, and $|z_{1}|\leqslant 4$, find the range of values for the real number $a$.

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