
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 that \( x_{1}, \cdots, x_{n} \) are all real numbers within the interval \(\left(\frac{1}{4}, 1\right)\), find the minimum value of the sum \( \sum_{k=1}^{n} \log _{x_{4}}\left(x_{k+1} - \frac{1}{4}\right) \), where \( x_{n+1} = x_{1} \).

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