
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 $f(x)=\log _{2}(4^{x}+1)+kx (k\in R)$ is an even function.

(1) Find the value of $k$;

(2) If the function $y=f(x)-x-a$ has no zero points, find the range of values for $a$;

(3) If the function $h(x)=2^{f(x)+x}+m\cdot 2^{x}-1, x\in[0,\log _{2}3]$ has a minimum value of $0$, find the value of the real number $m$.

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