
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 that \(4(\log_a y)^2 + 5(\log_b y)^2 = 10(\log y)^2\) where \(a\) and \(b\) are positive numbers different from 1, express the possible values for \(\log_b a\) in terms of logarithms.

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