
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 numbers \(\log _{\sqrt{\frac{x}{3}+3}}(6 x-14)\), \(\log _{6 x-14}(x-1)^{2}\), \(\log _{x-1}\left(\frac{x}{3}+3\right)\), for what \(x\) are two of these numbers equal and the third is less than them by 1?

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