
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
Determine the values of $a$ and $b$ such that $3(\log_a x)^2 + 5(\log_b x)^2 = \frac{10(\log x)^2}{\log a + \log b}$, where $x > 1$.
A) $b = a^{\frac{8}{3}}$
B) $b = a^{\frac{5 + \sqrt{10}}{3}}$
C) $b = a^{\frac{5 - \sqrt{10}}{3}}$
D) $b = a^{\frac{4}{3}}$

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