
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
Find all values of \( x \) for which one of the three given numbers \(\log _{x}\left(x-\frac{13}{6}\right)\), \(\log _{x-\frac{13}{6}}(x-3)\), and \(\log _{x-3} x\) is equal to the product of the other two.

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