
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 the function $f(x)= \begin{cases} 2^{x}+a, & x < 2 \\ a-x, & x\geqslant 2 \end{cases}$  
$(1)$ If $a=- \sqrt {2}$, then the zero of $f(x)$ is \_\_\_\_\_\_ .  
$(2)$ If $f(x)$ has no zero, then the range of the real number $a$ is \_\_\_\_\_\_ .

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