
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
(1) Calculate the value of the definite integral $\int_{-2}^{2}{\left| x^{2}-1 \right|dx}$.

(2) If the complex number $z_{1}=a+2i(a\in \mathbb{R})$, $z_{2}=3-4i$, and $\frac{z_{1}}{z_{2}}$ is a pure imaginary number, find $|z_{1}|$.

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