
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 $6(\log_c x)^2 + 5(\log_d x)^2 = \frac{12(\log x)^2}{\log c \log d}$, find the possible relationships between $c$ and $d$.
A) \( d = c^{\frac{5}{6 + \sqrt{6}}} \)
B) \( d = c^{\frac{5}{6 - \sqrt{6}}} \)
C) \( d = c^2 \)
D) \( d = c^{2/3} \)

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