
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
Let the function \( f(x) \) be monotonic on \((-\infty, +\infty)\) and satisfy \( f(x + y) = f(x) + f(y) \) with \( f(1) = -1 \). If \( f\left( k \log_{2} t \right) + f\left( \log_{2} t - \log_{2}{ }^{2} t - 2 \right) \) is always greater than 0 for any positive number \( t \), find the range of values for \( k \).

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