
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
Solve the inequality: 
\[ 8.57 \log_{3} \log_{4} \left(\frac{4x - 1}{x + 1}\right) - \log_{\frac{1}{3}} \log_{\frac{1}{4}} \left(\frac{x + 1}{4x - 1}\right) < 0. \]

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