
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
The sequence $\{ \log_k{a_n} \}$ is an arithmetic progression with a first term of 4 and a common difference of 2, where $k > 0$ and $k \neq 1$. Let $c_n = a_n \log_k{a_n}$. If every term in the sequence $\{c_n\}$ is less than the term that follows it, then the range of the real number $k$ is ______.

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