
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) Given that $i$ is the imaginary unit, and the complex number $z=\frac{m^2-4+(m+2)i}{\phantom{m^2-4+(m+2)i}}(m\in \mathbb{R})$ is a pure imaginary number, find $m=\_\_\_\_\_\_\_\_\_\_\_\_$

(2) Find the size of the angle of inclination of the line given by the parametric equations: $\begin{cases} x=1+t \\ y=1-t \end{cases} (t\text{ is a parameter})$

(3) Given $x+2y=1$, find the minimum value of ${2^{x}}+{4^{y}}=\_\_\_\_\_\_\_\_\_\_\_$

(4) Observe the following expressions: $1+ \frac{1}{{2}^{2}} < \frac{3}{2},1+ \frac{1}{{2}^{2}}+ \frac{2}{{3}^{2}} < \frac{5}{3},1+ \frac{1}{{2}^{2}}+ \frac{1}{{3}^{2}}+ \frac{1}{{4}^{2}} < \frac{7}{4},\cdots$ Based on these expressions, find the value of $1+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+\frac{1}{{{4}^{2}}}+\cdots + \frac{1}{{{2015}^{2}}} < \_\_\_\_\_\_\_\_\_\_\_\_\_$

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