
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 $f(x)=\log_{2}(16^{x}+k)-2x$ $(k\in\mathbb{R})$ is an even function.  
(1) Find $k$;  
(2) If the inequality $m-1\leqslant f(x)\leqslant 2m+\log_{2}17$ holds for all $x\in[-1, \frac{1}{2}]$, find the range of the real number $m$.

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