
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) Find the value of the definite integral $\int_{-2}^{1}|x^{2}-2|dx$.
(2) Given complex numbers $z_{1}=a+2i$ ($a \in \mathbb{R}$) and $z_{2}=3-4i$, if $\frac{z_{1}}{z_{2}}$ is a purely imaginary number, find $|z_{1}|$.

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