
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 a function $f(x)= \begin{cases} x+1 & 0\leqslant x\leqslant 1 \\ \frac{1}{2}\sin \left( \frac{\pi}{4}x \right)+ \frac{3}{2} & 1 < x\leqslant 4 \end{cases}$, if the inequality $f^{2}(x)-af(x)+2 < 0$ holds true for all $x\in[0,4]$, determine the range of the real number $a$.

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