
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
$$
f(x)=\log _{4}\left(4^{x}+1\right)+kx \quad (k \in \mathbf{R})
$$
is an even function.
1. Find the value of \( k \).
2. If the equation \( f(x)=\log _{4}\left(\frac{m}{2^{x}}-1\right) \) has a solution, find the range of the real number \( m \).

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