
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 $f(x) = \log_{4}(4^{x}+1) + kx$, where $k \in \mathbb{R}$, is an even function.
1. Find the value of $k$;
2. If the function $h(x) = 4^{f(x)+ \frac{x}{2}} + m \cdot 2^{x} - 1$, where $x \in [0, \log_{2}3]$, has a minimum value of 0, find the value of $m$;
3. If the graph of the function $y = f(x)$ and the line $y = \frac{1}{2}x + a$ have no intersection points, find the range of values for $a$.

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